Zaloguj się

Gotowe bibliografie tematyczne / Trivial zeros / Artykuły w czasopismach

Kliknij ten link, aby zobaczyć inne rodzaje publikacji na ten temat: Trivial zeros.

Artykuły w czasopismach na temat „Trivial zeros”

Autor: Grafiati

Data publikacji: 30 listopada 2024

Utwórz poprawne odniesienie w stylach APA, MLA, Chicago, Harvard i wielu innych

Wybierz rodzaj źródła:

Sprawdź 50 najlepszych artykułów w czasopismach naukowych na temat „Trivial zeros”.

Przycisk „Dodaj do bibliografii” jest dostępny obok każdej pracy w bibliografii. Użyj go – a my automatycznie utworzymy odniesienie bibliograficzne do wybranej pracy w stylu cytowania, którego potrzebujesz: APA, MLA, Harvard, Chicago, Vancouver itp.

Możesz również pobrać pełny tekst publikacji naukowej w formacie „.pdf” i przeczytać adnotację do pracy online, jeśli odpowiednie parametry są dostępne w metadanych.

Przeglądaj artykuły w czasopismach z różnych dziedzin i twórz odpowiednie bibliografie.

1

Bayer, Pilar. "La hipòtesi de Riemann: El gran repte pendent". Mètode Revista de difusió de la investigació, nr 8 (5.06.2018): 35. http://dx.doi.org/10.7203/metode.0.8903.

Pełny tekst źródła

Streszczenie:

The Riemann hypothesis is an unproven statement referring to the zeros of the Riemann zeta function. Bernhard Riemann calculated the first six non-trivial zeros of the function and observed that they were all on the same straight line. In a report published in 1859, Riemann stated that this might very well be a general fact. The Riemann hypothesis claims that all non-trivial zeros of the zeta function are on the the line x = 1/2. The more than ten billion zeroes calculated to date, all of them lying on the critical line, coincide with Riemann’s suspicion, but no one has yet been able to prove that the zeta function does not have non-trivial zeroes outside of this line.

Style APA, Harvard, Vancouver, ISO itp.

2

Lam Kai, Shun. "A Verification of Riemann Non-Trivial Zeros by Complex Analysis by Matlab™ Computation". European Journal of Statistics and Probability 11, nr 1 (15.01.2023): 69–83. http://dx.doi.org/10.37745/ejsp.2013/vol11n16983.

Pełny tekst źródła

Streszczenie:

With my most recent paper, I tried to prove the Riemann Hypothesis by catching out those contradictory parts of the non-trivial zeros. In the present paper, I will try to verify these known values of Riemann nontrivial zeros by first using U.S.A. Matlab coding with a list of well-organized complex analysis theories. At the same time, as the major core of my verification is just a mono-direction one (i.e. there may be a possibility of the missing non-trivial zeros although the residue value is zero), hence this author try to solve such problem by assuming that there are some other zeros existing between the two known zeros but the contradiction arises – as singularity implies the residue has a value with a multiple of 2πi. In addition, this author also apply the ingenious design (or a hybrid skill) with Feynman technique and Integration by parts to solve a special zeta function integral. Next, this author finds that one may consider those non-trivial zeros as a Fourier transform (or an impulse) between other normal complex numbers. The result is consistent with my previous papers in quantum physics [23], [25] for the electron jumps or reverse. Hence, we may get the (dirac) delta equation for Riemann Zeta. Then we may formulate our quantum circuit & computer. Finally, this author concludes all findings with an algorithm for searching, finer and checking the non-trivial zeros like below: Step 1: Use the computer software with some suitable program codes for an elementary search of feasible non-trivial zeta values among the closed real-complex plane interval – Method Matlab Simulation for searching zeta zeros; Step 2: Substitute back the values laying in the contour interval for zeta as found in Step 1 into the limit of ln(zeta(z))/((zeta'(z)) ) in order to adjust the answer in a finer and accurate way (just like the case of Newton’s method etc) with more decimal digitals – Method Ingenious Design for finer the zeta zero’s values; Step 3: Employ the Cauchy Residue Theorem for a check and hence confirm the previous found non-trivial zeta roots’ uniqueness without any zeta zeros laying in between the two consecutive zeta roots – Method Cauchy’s Residue for checking those already found zeta zeros.

Style APA, Harvard, Vancouver, ISO itp.

3

HASSEN, ABDUL, i HIEU D. NGUYEN. "A ZERO-FREE REGION FOR HYPERGEOMETRIC ZETA FUNCTIONS". International Journal of Number Theory 07, nr 04 (czerwiec 2011): 1033–43. http://dx.doi.org/10.1142/s1793042111004678.

Pełny tekst źródła

Streszczenie:

This paper investigates the location of "trivial" zeros of some hypergeometric zeta functions. Analogous to Riemann's zeta function, we demonstrate that they possess a zero-free region on a left-half complex plane, except for infinitely many zeros regularly spaced on the negative real axis.

Style APA, Harvard, Vancouver, ISO itp.

4

Platt, David J. "Isolating some non-trivial zeros of zeta". Mathematics of Computation 86, nr 307 (13.02.2017): 2449–67. http://dx.doi.org/10.1090/mcom/3198.

Pełny tekst źródła

Style APA, Harvard, Vancouver, ISO itp.

5

Ghisa, Dorin. "On the Non-Trivial Zeros of Dirichlet Functions". Advances in Pure Mathematics 11, nr 03 (2021): 187–204. http://dx.doi.org/10.4236/apm.2021.113014.

Pełny tekst źródła

Style APA, Harvard, Vancouver, ISO itp.

6

Silva, Sergio Da. "The Riemann Hypothesis: A Fresh and Experimental Exploration". Journal of Advances in Mathematics and Computer Science 39, nr 4 (2.04.2024): 100–112. http://dx.doi.org/10.9734/jamcs/2024/v39i41885.

Pełny tekst źródła

Streszczenie:

This research proposes a new approach to the Riemann Hypothesis, focusing on the interplay between prime gaps and the non-trivial zeros of the Riemann Zeta function. Utilizing various statistical models and experimental analysis techniques, three important insights are uncovered: 1) Granger causality tests reveal a predictive relationship in which past non-trivial zeros may predict future prime gaps; 2) Complex, nonlinear interactions between prime gaps and non-trivial zeros are identified, challenging simple linear correlations; and 3) Causal network analysis reveals intricate feedback-loop relationships. These findings contribute to a better understanding of prime number distribution and the Zeta function, opening up novel possibilities for further mathematical research. The study aims to motivate mathematicians towards a proof or disproof of the Riemann Hypothesis.

Style APA, Harvard, Vancouver, ISO itp.

7

Apostol, Tom M. "Note on the Trivial Zeros of Dirichlet L-Functions". Proceedings of the American Mathematical Society 94, nr 1 (maj 1985): 29. http://dx.doi.org/10.2307/2044944.

Pełny tekst źródła

Style APA, Harvard, Vancouver, ISO itp.

8

Rohrlich, David E. "Scarcity and abundance of trivial zeros in division towers". Journal of Algebraic Geometry 17, nr 4 (2008): 643–75. http://dx.doi.org/10.1090/s1056-3911-08-00462-1.

Pełny tekst źródła

Style APA, Harvard, Vancouver, ISO itp.

9

Benois, Denis. "Trivial zeros of -adic -functions at near-central points". Journal of the Institute of Mathematics of Jussieu 13, nr 3 (24.09.2013): 561–98. http://dx.doi.org/10.1017/s1474748013000261.

Pełny tekst źródła

Streszczenie:

AbstractUsing the$\ell $-invariant constructed in our previous paper we prove a Mazur–Tate–Teitelbaum-style formula for derivatives of$p$-adic$L$-functions of modular forms at trivial zeros. The novelty of this result is to cover the near-central point case. In the central point case our formula coincides with the Mazur–Tate–Teitelbaum conjecture proved by Greenberg and Stevens and by Kato, Kurihara and Tsuji at the end of the 1990s.

Style APA, Harvard, Vancouver, ISO itp.

10

Apostol, Tom M. "Note on the trivial zeros of Dirichlet $L$-functions". Proceedings of the American Mathematical Society 94, nr 1 (1.01.1985): 29. http://dx.doi.org/10.1090/s0002-9939-1985-0781049-8.

Pełny tekst źródła

Style APA, Harvard, Vancouver, ISO itp.

11

Suman, Shekhar, i Raman Kumar Das. "A NOTE ON AN EQUIVALENT OF THE RIEMANN HYPOTHESIS". JOURNAL OF RAMANUJAN SOCIETY OF MATHEMATICS AND MATHEMATICAL SCIENCES 10, nr 01 (30.12.2022): 97–102. http://dx.doi.org/10.56827/jrsmms.2022.1001.8.

Pełny tekst źródła

Streszczenie:

In this manuscript we denote by P ρ a sum over the non trivial zeros of Riemann zeta function (or over the zeros of Riemann’s xi function), where the zeros of multiplicity k are counted k times. We prove a result that the Riemann Hypothesis is true if and only if

Style APA, Harvard, Vancouver, ISO itp.

12

Sekatskii, Sergey. "On the Sums over Inverse Powers of Zeros of the Hurwitz Zeta Function and Some Related Properties of These Zeros". Symmetry 16, nr 3 (7.03.2024): 326. http://dx.doi.org/10.3390/sym16030326.

Pełny tekst źródła

Streszczenie:

Recently, we have applied the generalized Littlewood theorem concerning contour integrals of the logarithm of the analytical function to find the sums over inverse powers of zeros for the incomplete gamma and Riemann zeta functions, polygamma functions, and elliptical functions. Here, the same theorem is applied to study such sums for the zeros of the Hurwitz zeta function ζ(s,z), including the sum over the inverse first power of its appropriately defined non-trivial zeros. We also study some related properties of the Hurwitz zeta function zeros. In particular, we show that, for any natural N and small real ε, when z tends to n = 0, −1, −2… we can find at least N zeros of ζ(s,z) in the ε neighborhood of 0 for sufficiently small |z+n|, as well as one simple zero tending to 1, etc.

Style APA, Harvard, Vancouver, ISO itp.

13

soltan, Shaimaa said. "New Odd Numbers Identity and the None-trivial Zeros of Zeta Function". Journal of Mathematics Research 15, nr 2 (8.04.2023): 74. http://dx.doi.org/10.5539/jmr.v15n2p74.

Pełny tekst źródła

Streszczenie:

This paper is going to introduce a new identity unit circle function for complex plane specific for odd numbers. Second, we are going to show some properties of these new unit Identity function. Third, use this new unit Identity function to study the distribution of odd roots for sin term in zeta function but using the new identity function not Euler Identity to explain Riemann conjunction about the critical strip line and the none-trivial zeros along Re(S) = 0.5. Also, In an Introductory Analysis for the geometric functions Sin and Cos, we will visualize the inverse of geometric function Sin. Riemann's functional equation Then Zeta function will be zero At             is Zero for any complex number S. If exponential term is zero also when S = S + 0.5 where S is any complex number.

Style APA, Harvard, Vancouver, ISO itp.

14

Wong, Bertrand. "Non-trivial zeros of riemann zeta function and riemann hypothesis". Bulletin of Pure & Applied Sciences- Mathematics and Statistics 41e, nr 1 (2022): 88–99. http://dx.doi.org/10.5958/2320-3226.2022.00013.3.

Pełny tekst źródła

Style APA, Harvard, Vancouver, ISO itp.

15

BERGWEILER, WALTER, ALEXANDRE EREMENKO i AIMO HINKKANEN. "Entire functions with two radially distributed values". Mathematical Proceedings of the Cambridge Philosophical Society 165, nr 1 (4.04.2017): 93–108. http://dx.doi.org/10.1017/s0305004117000305.

Pełny tekst źródła

Streszczenie:

AbstractWe study entire functions whose zeros and one-points lie on distinct finite systems of rays. General restrictions on these rays are obtained. Non-trivial examples of entire functions with zeros and one-points on different rays are constructed, using the Stokes phenomenon for second order linear differential equations.

Style APA, Harvard, Vancouver, ISO itp.

16

Hemingway, Xian. "The Generalized Riemann Hypothesis on elliptic complex fields". AIMS Mathematics 8, nr 11 (2023): 25772–803. http://dx.doi.org/10.3934/math.20231315.

Pełny tekst źródła

Streszczenie:

<abstract><p>In this paper, we will introduce a new algebraic system called the elliptic complex, and consider the distribution of zeros of the function $ L(s, \chi) $ in the corresponding complex plane. The key to this article is to discover the limiting case of the Generalized Riemann Hypothesis on elliptic complex fields and, taking a series of elliptic complex fields as variables, to study the ordinary properties of their distributions about the non-trivial zeros of $ L(s, \chi) $. It is on the basis of these considerations that we will draw the following conclusions. First, the zeros of the function $ L(s, \chi) $ on any two elliptic complex planes correspond one-to-one. Then, all non-trivial zeros of the $ L(s, \chi) $ function on each elliptic complex plane are distributed on the critical line $ \Re(s) = {1\over 2} $ due to the critical case of the Generalized Riemann Hypothesis. Ultimately we proved the Generalized Riemann Hypothesis.</p></abstract>

Style APA, Harvard, Vancouver, ISO itp.

17

FARAG, HANY M. "DIRICHLET TRUNCATIONS OF THE RIEMANN ZETA FUNCTION IN THE CRITICAL STRIP POSSESS ZEROS NEAR EVERY VERTICAL LINE". International Journal of Number Theory 04, nr 04 (sierpień 2008): 653–62. http://dx.doi.org/10.1142/s1793042108001596.

Pełny tekst źródła

Streszczenie:

We study the zeros of the finite truncations of the alternating Dirichlet series expansion of the Riemann zeta function in the critical strip. We do this with an (admittedly highly) ambitious goal in mind. Namely, that this series converges to the zeta function (up to a trivial term) in the critical strip and our hope is that if we can obtain good estimates for the zeros of these approximations it may be possible to generalize some of the results to zeta itself. This paper is a first step towards this goal. Our results show that these finite approximations have zeros near every vertical line (so no vertical strip in this region is zero-free). Furthermore, we give upper bounds for the imaginary parts of the zeros (the real parts are pinned). The bounds are numerically very large. Our tools are: the inverse mapping theorem (for a perturbative argument), the prime number theorem (for counting primes), elementary geometry (for constructing zeros of a related series), and a quantitative version of Kronecker's theorem to go from one series to another.

Style APA, Harvard, Vancouver, ISO itp.

18

TOURIGNY, DAVID S. "RIEMANN ZEROS AND THE INVERSE PHASE PROBLEM". Modern Physics Letters B 27, nr 26 (10.10.2013): 1350187. http://dx.doi.org/10.1142/s021798491350187x.

Pełny tekst źródła

Streszczenie:

Finding a universal method of crystal structure solution and proving the Riemann hypothesis are two outstanding challenges in apparently unrelated fields. For centro-symmetric crystals however, a connection arises as the result of a statistical approach to the inverse phase problem. It is shown that parameters of the phase distribution are related to the non-trivial Riemann zeros by a Mellin transform.

Style APA, Harvard, Vancouver, ISO itp.

19

Shavala, O. "ON THE CONSTRUCTION OF SOLUTIONS OF DIFFERENTIAL EQUATIONS ACCORDING TO GIVEN SEQUENCES OF ZEROS AND CRITICAL POINTS". Bukovinian Mathematical Journal 11, nr 1 (2023): 134–37. http://dx.doi.org/10.31861/bmj2023.01.12.

Pełny tekst źródła

Streszczenie:

A part of the theory of differential equations in the complex plane $\mathbb C$ is the study of their solutions. To obtain them sometimes researchers can use local expand of solution in the integer degrees of an independent variable. In more difficult cases received local expand in fractional degrees of an independent variable, on so-called Newton - Poiseux series. A row of mathematicians for integration of linear differential equations applied a method of so-called generalized degree series, where meets irrational, in general real degree of an independent variable. One of the directions of the theory of differential equations in the complex plane $\mathbb C$ is the construction a function $f$ according given sequence of zeros or poles, zeros of the derivative $f'$ and then find a differential equation for which this function be solution. Some authors studied sequences of zeros of solutions of the linear differential equation \begin{equation*} f''+Af=0, \end{equation*} where $A$ is entire or analytic function in a disk ${\rm \{ z:|z| < 1\} }$. In addition to the case when the above-mentioned differential equation has the non-trivial solution with given zero-sequences it is possible for consideration the case, when this equation has a solution with a given sequence of zeros (poles) and critical points. In this article we consider the question when the above-mentioned differential equation has the non-trivial solution $f$ such that $f^{1/\alpha}$, $\alpha \in {\mathbb R}\backslash \{ 0;-1\} $ is meromorphic function without zeros with poles in given sequence and the derivative of solution $f'$ has zeros in other given sequence, where $A$ is meromorphic function. Let's note, that representation of function by Weierstrass canonical product is the basic element for researches in the theory of the entire functions. Further we consider the question about construction of entire solution $f$ of the differential equation \begin{equation*} f^{(n)} +Af^{m} =0, \quad n,m\in {\mathbb N}, \end{equation*} where $A$ is meromorphic function such that $f$ has zeros in given sequence and the derivative of solution $f'$ has zeros in other given sequence.

Style APA, Harvard, Vancouver, ISO itp.

20

Özlük, Ali E., i C. Snyder. "Small zeros of quadratic L-functions". Bulletin of the Australian Mathematical Society 47, nr 2 (kwiecień 1993): 307–19. http://dx.doi.org/10.1017/s0004972700012545.

Pełny tekst źródła

Streszczenie:

We study the distribution of the imaginary parts of zeros near the real axis of quadratic L-functions. More precisely, let K(s) be chosen so that |K(1/2 ± it)| is rapidly decreasing as t increases. We investigate the asymptotic behaviour ofas D → ∞. Here denotes the sum over the non-trivial zeros p = 1/2 + iγ of the Dirichlet L-function L(s, χd), and χd = () is the Kronecker symbol. The outer sum is over all fundamental discriminants d that are in absolute value ≤ D. Assuming the Generalized Riemann Hypothesis, we show that for

Style APA, Harvard, Vancouver, ISO itp.

21

Lindner, A. "Non-trivial zeros of the Wigner (3j) and Racah (6j) coefficients". Journal of Physics A: Mathematical and General 18, nr 15 (21.10.1985): 3071–72. http://dx.doi.org/10.1088/0305-4470/18/15/029.

Pełny tekst źródła

Style APA, Harvard, Vancouver, ISO itp.

22

Deza, Elena, i Lidiya Varukhina. "REPRESENTATIONS OF ARITHMETIC SUMS OVER NON-TRIVIAL ZEROS OF THE ZETA FUNCTION". Asian-European Journal of Mathematics 01, nr 04 (grudzień 2008): 509–19. http://dx.doi.org/10.1142/s1793557108000412.

Pełny tekst źródła

Streszczenie:

We obtain representations over non-trivial zeros of zeta function for two arithmetic functions ψ1(x) = ∑n≤x (x - n)Λ(n) and [Formula: see text]. This result is similar to classical representations of such kind for the Chebyshev functionψ(x) = ∑n≤x Λ(n).

Style APA, Harvard, Vancouver, ISO itp.

23

KANEKO, SATORU, HIDEYUKI SAWANAKA, TAKAYA SHINGAI, MORIMITSU TANIMOTO i KOICHI YOSHIOKA. "FLAVOR SYMMETRY AND VACUUM ALIGNED MASS TEXTURES". International Journal of Modern Physics E 16, nr 05 (czerwiec 2007): 1427–36. http://dx.doi.org/10.1142/s0218301307006782.

Pełny tekst źródła

Streszczenie:

A texture-zeros is an approach to reduce the number of free parameters in Yukawa couplings and it is one of the most attractive ones. In our paper, we discuss the origin of zero-structure in texture-zeros by S3 flavor symmetry approach. Some of electroweak doublet Higgs fields have vanishing vacuum expectation value (VEV) which leads to vanishing elements in quark and lepton mass matrices. Then, the structure of supersymmetric scalar potential is analyzed and Higgs fields have non-trivial S3 charges. As a prediction of our paper, a lower bound of a MNS matrix element, Ue3 ≥ 0.04, is obtained. The suppression of flavor-changing neutral currents (FCNC) mediated by the Higgs fields is discussed and lower bounds of the Higgs masses are derived.

Style APA, Harvard, Vancouver, ISO itp.

24

Ting, John Y. C. "Key Role of Dimensional Analysis Homogeneity in Proving Riemann Hypothesis and Providing Explanations on the Closely Related Gram Points". Journal of Mathematics Research 8, nr 4 (25.07.2016): 1. http://dx.doi.org/10.5539/jmr.v8n4p1.

Pełny tekst źródła

Streszczenie:

Riemann zeta function is the famous complex number infinite series consisting of a real and an imaginary part. Non-trivial zeros and Gram points are best seen as mathematically derived entities of this function when its variable Sigma has a value of $\frac{1}{2}$. The presence [but not the actual locations] of the complete set of infinite non-trivial zeros is characterized by the criterion that the sum total of the simultaneous real and imaginary parts in Riemann zeta function equates to zero. In an identical manner this slightly altered criterion for the presence [but not the actual locations] of the complete set of infinite Gram points is that this 'sum total' now refer to the lesser requirement that only the individual imaginary part in Riemann zeta function equates to zero. The key role played by Dimensional analysis homogeneity to rigorously prove Riemann conjecture/hypothesis has been fully outlined in our landmark research paper published earlier on Page 9 - 21 in the preceding Volume 8, Number 3, June 2016 issue of this journal. Those resulting methodology previously employed by us are now mathematically used in an analogical procedure to delineate its role in successfully supplying crucial explanations for Gram points. In this research article, we use the notation \{Non-critical lines\}-Gram points to signify those 'near-identical' (virtual) Gram points when Sigma value is not $\frac{1}{2}$.

Style APA, Harvard, Vancouver, ISO itp.

25

Wang, Wei, Yanjie Zhu, Zhuoxu Cui i Dong Liang. "Is Each Layer Non-trivial in CNN? (Student Abstract)". Proceedings of the AAAI Conference on Artificial Intelligence 35, nr 18 (18.05.2021): 15915–16. http://dx.doi.org/10.1609/aaai.v35i18.17954.

Pełny tekst źródła

Streszczenie:

Convolutional neural network (CNN) models have achieved great success in many fields. With the advent of ResNet, networks used in practice are getting deeper and wider. However, is each layer non-trivial in networks? To answer this question, we trained a network on the training set, then we replace the network convolution kernels with zeros and test the result models on the test set. We compared experimental results with baseline and showed that we can reach similar or even the same performances. Although convolution kernels are the cores of networks, we demonstrate that some of them are trivial and regular in ResNet.

Style APA, Harvard, Vancouver, ISO itp.

26

Csoka, Levente. "The Fourier Transform of the Non-Trivial Zeros of the Zeta Function". Journal of Advances in Applied & Computational Mathematics 4, nr 1 (2.06.2018): 23–25. http://dx.doi.org/10.15377/2409-5761.2017.04.4.

Pełny tekst źródła

Style APA, Harvard, Vancouver, ISO itp.

27

Somvanshi, Manvendra. "On Trivial Zeros of Zeta Function and Problems with the Analytic Continuation". International Journal of Mathematics Trends and Technology 55, nr 6 (25.03.2018): 430–33. http://dx.doi.org/10.14445/22315373/ijmtt-v55p557.

Pełny tekst źródła

Style APA, Harvard, Vancouver, ISO itp.

28

Laurinčikas, Antanas. "Non-trivial zeros of the Riemann zeta-function and joint universality theorems". Journal of Mathematical Analysis and Applications 475, nr 1 (lipiec 2019): 385–402. http://dx.doi.org/10.1016/j.jmaa.2019.02.047.

Pełny tekst źródła

Style APA, Harvard, Vancouver, ISO itp.

29

Kiguradze, Ivan. "Beurling–Borg Type Theorem for Two-Dimensional Linear Differential Systems". gmj 15, nr 4 (grudzień 2008): 677–82. http://dx.doi.org/10.1515/gmj.2008.677.

Pełny tekst źródła

Streszczenie:

Abstract For the two-dimensional linear differential system with Lebesgue integrable coefficients 𝑝𝑖𝑘 : [𝑎, 𝑏] → ℝ (𝑖 = 1, 2), a Beurling–Borg type theorem is proved on an upper estimate of the number of zeros of an arbitrary non-trivial solution.

Style APA, Harvard, Vancouver, ISO itp.

30

Bartušek, Miroslav. "On Structure of Solutions of a System of Four Differential Inequalities". gmj 2, nr 3 (czerwiec 1995): 225–36. http://dx.doi.org/10.1515/gmj.1995.225.

Pełny tekst źródła

Streszczenie:

Abstract The aim of the paper is to study a global structure of solutions of four differential inequalities with respect to their zeros. The structure of an oscillatory solution is described, and the number of points with trivial Cauchy conditions is investigated.

Style APA, Harvard, Vancouver, ISO itp.

31

He, Yang-Hui, Vishnu Jejjala i Djordje Minic. "Eigenvalue Density, Li's Positivity, and the Critical Strip". inSTEMM Journal 1, S1 (15.07.2022): 1–14. http://dx.doi.org/10.56725/instemm.v1is1.23.

Pełny tekst źródła

Streszczenie:

We rewrite the zero-counting formula within the critical strip of the Riemann zeta function as a cumulative density distribution;this subsequently allows us to formally derive an integral expression for the Li coefficients associated with the Riemann Xi-function which, in particular, indicate that their positivity criterion is obeyed, whereby entailing the criticality of the non-trivial zeros. We conjecture the validity of this and related expressions without the need for the Riemann Hypothesis and also offer a physical interpretation of the result and discuss the Hilbert-Polya approach.

Style APA, Harvard, Vancouver, ISO itp.

32

Heath-Brown, D. R. "Zeros of systems of 𝔭-adic quadratic forms". Compositio Mathematica 146, nr 2 (22.01.2010): 271–87. http://dx.doi.org/10.1112/s0010437x09004497.

Pełny tekst źródła

Streszczenie:

AbstractWe show that a system of r quadratic forms over a 𝔭-adic field in at least 4r+1 variables will have a non-trivial zero as soon as the cardinality of the residue field is large enough. In contrast, the Ax–Kochen theorem [J. Ax and S. Kochen, Diophantine problems over local fields. I, Amer. J. Math. 87 (1965), 605–630] requires the characteristic to be large in terms of the degree of the field over ℚp. The proofs use a 𝔭-adic minimization technique, together with counting arguments over the residue class field, based on considerations from algebraic geometry.

Style APA, Harvard, Vancouver, ISO itp.

33

Foote, Richard, i V. Kumar Murty. "Zeros and poles of Artin L-series". Mathematical Proceedings of the Cambridge Philosophical Society 105, nr 1 (styczeń 1989): 5–11. http://dx.doi.org/10.1017/s0305004100001316.

Pełny tekst źródła

Streszczenie:

Let E/F be a finite normal extension of number fields with Galois group G. For each virtual character χ of G, denote by L(s, χ) = L(s, χ, F) the Artin L-series attached to χ. It is defined for Re (s) > 1 by an Euler product which is absolutely convergent, making it holomorphic in this half plane. Artin's holomorphy conjecture asserts that, if χ is a character, L(s, χ) has a continuation to the entire s-plane, analytic except possibly for-a pole at s = 1 of multiplicity equal to 〈χ, 1〉, where 1 denotes the trivial character. A well-known group-theoretic result of Brauer implies that L(s, χ) has a meromorphic continuation for all s.

Style APA, Harvard, Vancouver, ISO itp.

34

Lagarias, Jeffrey C., i Brad Rodgers. "HIGHER CORRELATIONS AND THE ALTERNATIVE HYPOTHESIS". Quarterly Journal of Mathematics 71, nr 1 (23.01.2020): 257–80. http://dx.doi.org/10.1093/qmathj/haz043.

Pełny tekst źródła

Streszczenie:

Abstract The Alternative Hypothesis (AH) concerns a hypothetical and unlikely picture of how zeros of the Riemann zeta function are spaced, which one would like to rule out. In the Alternative Hypothesis, the renormalized distance between non-trivial zeros is supposed to always lie at a half integer. It is known that the Alternative Hypothesis is compatible with what is known about the pair correlation function of zeta zeros. We ask whether what is currently known about higher correlation functions of the zeros is sufficient to rule out the Alternative Hypothesis and show by construction of an explicit counterexample point process that it is not. A similar result was recently independently obtained by Tao, using slightly different methods. We also apply the ergodic theorem to this point process to show there exists a deterministic collection of points lying in $\tfrac{1}{2}\mathbb{Z}$, which satisfy the Alternative Hypothesis spacing, but mimic the local statistics that are currently known about zeros of the zeta function.

Style APA, Harvard, Vancouver, ISO itp.

35

Šiaučiūnas, Darius, Raivydas Šimėnas i Monika Tekorė. "Approximation of Analytic Functions by Shifts of Certain Compositions". Mathematics 9, nr 20 (14.10.2021): 2583. http://dx.doi.org/10.3390/math9202583.

Pełny tekst źródła

Streszczenie:

In the paper, we obtain universality theorems for compositions of some classes of operators in multidimensional space of analytic functions with a collection of periodic zeta-functions. The used shifts of periodic zeta-functions involve the sequence of imaginary parts of non-trivial zeros of the Riemann zeta-function.

Style APA, Harvard, Vancouver, ISO itp.

36

O'MALLEY, ROBERT E. "NAIVE SINGULAR PERTURBATION THEORY". Mathematical Models and Methods in Applied Sciences 11, nr 01 (luty 2001): 119–31. http://dx.doi.org/10.1142/s0218202501000787.

Pełny tekst źródła

Streszczenie:

The paper demonstrates, via extremely simple examples, the shocks, spikes, and initial layers that arise in solving certain singularly perturbed initial value problems for first-order ordinary differential equations. As examples from stability theory, they are basic to many asymptotic techniques. First, we note that limiting solutions of linear homogeneous equations [Formula: see text] on t≥0 are specified by the zeros of [Formula: see text], rather than by the turning points where a(t) becomes zero. Furthermore, solutions to the solvable equations [Formula: see text] for k=1, 2 or 3 can feature canards, where the trivial limit continues to apply after it becomes repulsive. Limiting solutions of the separable equation [Formula: see text] may likewise involve switchings between the zeros of c(x) located immediately above and below x(0), if they exist, at zeros of A(t). Finally, limiting solutions of many other problems follow by using asymptotic expansions for appropriate special functions. For example, solutions of [Formula: see text] can be given in terms of the Bessel functions Kj(t4/4ε) and Ij(t4/4ε) for j=3/8 and -5/8.

Style APA, Harvard, Vancouver, ISO itp.

37

Arias de Reyna, Juan, i Jan van de Lune. "On the exact location of the non-trivial zeros of Riemann's zeta function". Acta Arithmetica 163, nr 3 (2014): 215–45. http://dx.doi.org/10.4064/aa163-3-3.

Pełny tekst źródła

Style APA, Harvard, Vancouver, ISO itp.

38

KELLIHER, JAMES P., i RIAD MASRI. "Analytic continuation of multiple Hurwitz zeta functions". Mathematical Proceedings of the Cambridge Philosophical Society 145, nr 3 (listopad 2008): 605–17. http://dx.doi.org/10.1017/s0305004107001028.

Pełny tekst źródła

Streszczenie:

AbstractWe use a variant of a method of Goncharov, Kontsevich and Zhao [5, 16] to meromorphically continue the multiple Hurwitz zeta function to $\mathbb{C}^{d}$, to locate the hyperplanes containing its possible poles and to compute the residues at the poles. We explain how to use the residues to locate trivial zeros of $\zeta_{d}(s;\theta)$.

Style APA, Harvard, Vancouver, ISO itp.

39

Laurinčikas, Antanas, i Darius Šiaučiūnas. "Universality in Short Intervals of the Riemann Zeta-Function Twisted by Non-Trivial Zeros". Mathematics 8, nr 11 (3.11.2020): 1936. http://dx.doi.org/10.3390/math8111936.

Pełny tekst źródła

Streszczenie:

Let 0<γ1<γ2<⋯⩽γk⩽⋯ be the sequence of imaginary parts of non-trivial zeros of the Riemann zeta-function ζ(s). Using a certain estimate on the pair correlation of the sequence {γk} in the intervals [N,N+M] with N1/2+ε⩽M⩽N, we prove that the set of shifts ζ(s+ihγk), h>0, approximating any non-vanishing analytic function defined in the strip {s∈C:1/2<Res<1} with accuracy ε>0 has a positive lower density in [N,N+M] as N→∞. Moreover, this set has a positive density for all but at most countably ε>0. The above approximation property remains valid for certain compositions F(ζ(s)).

Style APA, Harvard, Vancouver, ISO itp.

40

Guillory, Carroll. "A Characterization of a Sparse Blaschke Product". Canadian Mathematical Bulletin 32, nr 4 (1.12.1989): 385–90. http://dx.doi.org/10.4153/cmb-1989-056-0.

Pełny tekst źródła

Streszczenie:

AbstractWe give a characterization of a sparse Blaschke product b in terms of the separation of support sets of its zeros in M(H∞ + C) and the structure of the nonanalytic points. We use this characterization to give a sufficient condition on an interpolating Blaschke product q to have the following property: there exists a non trivial Gleason part P on which q is nonzero and less than one.

Style APA, Harvard, Vancouver, ISO itp.

41

Balčiūnas, Aidas, Virginija Garbaliauskienė, Julija Karaliūnaitė, Renata Macaitienė, Jurgita Petuškinaitė i Audronė Rimkevičienė. "JOINT DISCRETE APPROXIMATION OF A PAIR OF ANALYTIC FUNCTIONS BY PERIODIC ZETA-FUNCTIONS". Mathematical Modelling and Analysis 25, nr 1 (13.01.2020): 71–87. http://dx.doi.org/10.3846/mma.2020.10450.

Pełny tekst źródła

Streszczenie:

In the paper, the problem of simultaneous approximation of a pair of analytic functions by a pair of discrete shifts of the periodic and periodic Hurwitz zeta-function is considered. The above shifts are deﬁned by using the sequence of imaginary parts of non-trivial zeros of the Riemann zeta-function. For the proof of approximation theorems, a weak form of the Montgomery pair correlation conjecture is applied.

Style APA, Harvard, Vancouver, ISO itp.

42

França, Guilherme, i André LeClair. "Some Riemann Hypotheses from random walks over primes". Communications in Contemporary Mathematics 20, nr 07 (14.10.2018): 1750085. http://dx.doi.org/10.1142/s0219199717500857.

Pełny tekst źródła

Streszczenie:

The aim of this paper is to investigate how various Riemann Hypotheses would follow only from properties of the prime numbers. To this end, we consider two classes of [Formula: see text]-functions, namely, non-principal Dirichlet and those based on cusp forms. The simplest example of the latter is based on the Ramanujan tau arithmetic function. For both classes, we prove that if a particular trigonometric series involving sums of multiplicative characters over primes is [Formula: see text], then the Euler product converges in the right half of the critical strip. When this result is combined with the functional equation, the non-trivial zeros are constrained to lie on the critical line. We argue that this [Formula: see text] growth is a consequence of the series behaving like a one-dimensional random walk. Based on these results, we obtain an equation which relates every individual non-trivial zero of the [Formula: see text]-function to a sum involving all the primes. Finally, we briefly mention important differences for principal Dirichlet [Formula: see text]-functions due to the existence of the pole at [Formula: see text], in which the Riemann [Formula: see text]-function is a particular case.

Style APA, Harvard, Vancouver, ISO itp.

43

ODŽAK, ALMASA, i LEJLA SMAJLOVIĆ. "ON INTERPOLATION FUNCTIONS FOR GENERALIZED Li COEFFICIENTS IN THE SELBERG CLASS". International Journal of Number Theory 07, nr 03 (maj 2011): 771–92. http://dx.doi.org/10.1142/s1793042111004356.

Pełny tekst źródła

Streszczenie:

We prove that there exists an entire complex function of order one and finite exponential type that interpolates the Li coefficients λF(n) attached to a function F in the class [Formula: see text] that contains both the Selberg class of functions and (unconditionally) the class of all automorphic L-functions attached to irreducible, cuspidal, unitary representations of GL n(ℚ). We also prove that the interpolation function is (essentially) unique, under generalized Riemann hypothesis. Furthermore, we obtain entire functions of order one and finite exponential type that interpolate both archimedean and non-archimedean contribution to λF(n) and show that those functions can be interpreted as zeta functions built, respectively, over trivial zeros and all zeros of a function [Formula: see text].

Style APA, Harvard, Vancouver, ISO itp.

44

Alvarez, P. D. "Exact partition function of the Potts model on the Sierpinski gasket and the Hanoi lattice". Journal of Statistical Mechanics: Theory and Experiment 2024, nr 8 (2.08.2024): 083101. http://dx.doi.org/10.1088/1742-5468/ad64bc.

Pełny tekst źródła

Streszczenie:

Abstract We present an analytic study of the Potts model partition function on the Sierpinski and Hanoi lattices, which are self-similar lattices of triangular shape with non integer Hausdorff dimension. Both lattices are examples of non-trivial thermodynamics in less than two dimensions, where mean field theory does not apply. We used and explain a method based on ideas of graph theory and renormalization group theory to derive exact equations for appropriate variables that are similar to the restricted partition functions. We benchmark our method with Metropolis Monte Carlo simulations. The analysis of fixed points reveals information of location of the Fisher zeros and we provide a conjecture about the location of zeros in terms of the boundary of the basins of attraction.

Style APA, Harvard, Vancouver, ISO itp.

45

Balčiūnas, Aidas, Violeta Franckevič, Virginija Garbaliauskienė, Renata Macaitienė i Audronė Rimkevičienė. "UNIVERSALITY OF ZETA-FUNCTIONS OF CUSP FORMS AND NON-TRIVIAL ZEROS OF THE RIEMANN ZETA-FUNCTION". Mathematical Modelling and Analysis 26, nr 1 (18.01.2021): 82–93. http://dx.doi.org/10.3846/mma.2021.12447.

Pełny tekst źródła

Streszczenie:

It is known that zeta-functions ζ(s,F) of normalized Hecke-eigen cusp forms F are universal in the Voronin sense, i.e., their shifts ζ(s + iτ,F), τ R, approximate a wide class of analytic functions. In the paper, under a weak form of the Montgomery pair correlation conjecture, it is proved that the shifts ζ(s+iγkh,F), where γ1 < γ2 < ... is a sequence of imaginary parts of non-trivial zeros of the Riemann zeta function and h > 0, also approximate a wide class of analytic functions.

Style APA, Harvard, Vancouver, ISO itp.

46

Matiyasevich, Yu V. "A relationship between certain sums over trivial and nontrivial zeros of the Riemann zeta-function". Mathematical Notes of the Academy of Sciences of the USSR 45, nr 2 (luty 1989): 131–35. http://dx.doi.org/10.1007/bf01158058.

Pełny tekst źródła

Style APA, Harvard, Vancouver, ISO itp.

47

CASTRO, CARLOS, i JORGE MAHECHA. "FRACTAL SUPERSYMMETRIC QM, GEOMETRIC PROBABILITY AND THE RIEMANN HYPOTHESIS". International Journal of Geometric Methods in Modern Physics 01, nr 06 (grudzień 2004): 751–93. http://dx.doi.org/10.1142/s0219887804000393.

Pełny tekst źródła

Streszczenie:

The Riemann's hypothesis (RH) states that the nontrivial zeros of the Riemann zeta-function are of the form sn=1/2+iλn. Earlier work on the RH based on supersymmetric QM, whose potential was related to the Gauss–Jacobi theta series, allows us to provide the proper framework to construct the well-defined algorithm to compute the density of zeros in the critical line, which would complement the existing formulas in the literature for the density of zeros in the critical strip. Geometric probability theory furnishes the answer to the difficult question whether the probability that the RH is true is indeed equal to unity or not. To test the validity of this geometric probabilistic framework to compute the probability if the RH is true, we apply it directly to the the hyperbolic sine function sinh (s) case which obeys a trivial analog of the RH (the HSRH). Its zeros are equally spaced in the imaginary axis sn=0+inπ. The geometric probability to find a zero (and an infinity of zeros) in the imaginary axis is exactly unity. We proceed with a fractal supersymmetric quantum mechanical (SUSY-QM) model implementing the Hilbert–Polya proposal to prove the RH by postulating a Hermitian operator that reproduces all the λn for its spectrum. Quantum inverse scattering methods related to a fractal potential given by a Weierstrass function (continuous but nowhere differentiable) are applied to the fractal analog of the Comtet–Bandrauk–Campbell (CBC) formula in SUSY QM. It requires using suitable fractal derivatives and integrals of irrational order whose parameter β is one-half the fractal dimension (D=1.5) of the Weierstrass function. An ordinary SUSY-QM oscillator is also constructed whose eigenvalues are of the form λn=nπ and which coincide with the imaginary parts of the zeros of the function sinh (s). Finally, we discuss the relationship to the theory of 1/f noise.

Style APA, Harvard, Vancouver, ISO itp.

48

Laurinčikas, Antanas. "Zeros of the Riemann zeta-function in the discrete universality of the Hurwitz zeta-function". Studia Scientiarum Mathematicarum Hungarica 57, nr 2 (czerwiec 2020): 147–64. http://dx.doi.org/10.1556/012.2020.57.2.1460.

Pełny tekst źródła

Streszczenie:

AbstractLet 0 < γ1 < γ2 < ··· ⩽ ··· be the imaginary parts of non-trivial zeros of the Riemann zeta-function. In the paper, we consider the approximation of analytic functions by shifts of the Hurwitz zeta-function ζ(s + iγkh, α), h > 0, with parameter α such that the set {log(m + α): m ∈ } is linearly independent over the field of rational numbers. For this, a weak form of the Montgomery conjecture on the pair correlation of {γk} is applied.

Style APA, Harvard, Vancouver, ISO itp.

49

Tanackov, Ilija, i Željko Stević. "Calculation of the value of the critical line using multiple zeta functions". AIMS Mathematics 8, nr 6 (2023): 13556–71. http://dx.doi.org/10.3934/math.2023688.

Pełny tekst źródła

Streszczenie:

<abstract> <p>Newton's identities of an infinite polynomial with complex-conjugate roots <italic>n</italic><sup><italic>−(</italic>σ+<italic>it</italic>)</sup> and <italic>n</italic><sup><italic>−(</italic>σ<italic>−it</italic>)</sup> are multiple zeta functions for <italic>n</italic>∈[1, ∞), σ∈R and <italic>t</italic>∈R. All Newton's identities can be represented by Macdonald determinants. In a special case of the Riemann hypothesis, the multiple zeta function of the first order is equal to zero, ζ(σ+<italic>it</italic>)+ζ(σ−<italic>it</italic>) = 0. The special case includes all non-trivial zeros. The value of the last, infinite multiple zeta function, in the special case, changes the structure of the determinant that can be calculated. The result is the reciprocal of the factorial value (<italic>n</italic>!)<sup>−1</sup>. The general value of the infinite multiple zeta function is calculated based on Vieta's rules and is equal to (<italic>n</italic>!)<sup>−2σ</sup>. The identity based on the relation of the special case and the general case (<italic>n</italic>!)<sup>−1</sup> = (<italic>n</italic>!)<sup>−2σ</sup> is reduced to the equation −1 = −2σ. The value of the critical line for all non-trivial zeros is singular, σ = ½.</p> </abstract>

Style APA, Harvard, Vancouver, ISO itp.

50

Shun, Lam Kai. "The Quantized Constants with Remmen’s Scattering Amplitude to Explain Riemann Zeta Zeros". International Journal of English Language Teaching 11, nr 4 (15.04.2023): 20–33. http://dx.doi.org/10.37745/ijelt.13/vol11n42033.

Pełny tekst źródła

Streszczenie:

Riemann Hypothesis has been proposed by Bernhard Riemann since year 1859. Nowadays, there are lots of proof or disproof all over the internet society or the academic professional authority etc. However, none of them is accepted by the Clay’s Mathematics Institute for her Millennium Prize. In the past few months, this author discovered that there may be a correlation exists between the real and imaginary parts of Riemann Zeta function for the first 10 non-trivial zeros of the Riemann function etc. Indeed, when one tries to view the correlation relationship as a constant like the Planck’s one. Then we may show that Riemann Zeta zeros are indeed discrete quantum energy levels or the discrete spectrum as electrons falling from some bound quantum state to a lower energy state (or Quantum Field Theory). That may be further explained by Remmen’s scattering amplitude or the S-matrix. We may approximate the S-matrix by applying the HKLam theory to it and predict the scattering amplitude or even the Riemann Zeta non-trival zeros etc. By the way, the key researching equations or formula in the following content will be around the Taylor expansion of the Riemann Zeta function, their convergence etc. In additional, I will also investigate the (*’’) as shown below: ∏_(i=1)^∞▒(z-z_i ) = ξ(0.5 + i*t) = (∑_(n=1)^∞▒1)⁄n^((0.5+i*t) ) = ∏_(j=1)^∞▒(1-1⁄(p_j^((0.5+i*t) ) ))^(-1) ------------ (*’’) as we may find the existence of some constants like the Planck’s one. For the application of the aforementioned scholarly outcome, it is well-known that if one can find the pattern of the appearance to the prime number and hence break the public key cryptography in the everyday usage of information technology security etc.

Style APA, Harvard, Vancouver, ISO itp.

Oferujemy zniżki na wszystkie plany premium dla autorów, których prace zostały uwzględnione w tematycznych zestawieniach literatury. Skontaktuj się z nami, aby uzyskać unikalny kod promocyjny!