Готові списки джерел за темами / Von Mangoldt function

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Добірка наукової літератури з теми "Von Mangoldt function"

Автор: Grafiati
Опубліковано: 8 березня 2025

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Статті в журналах з теми "Von Mangoldt function"

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Bienvenu, Pierre-Yves. "Asymptotics for some polynomial patterns in the primes." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 149, no. 5 (January 17, 2019): 1241–90. http://dx.doi.org/10.1017/prm.2018.52.

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AbstractWe prove asymptotic formulae for sums of the form $$\sum\limits_{n\in {\open z}^d\cap K} {\prod\limits_{i = 1}^t {F_i} } (\psi _i(n)),$$where K is a convex body, each Fi is either the von Mangoldt function or the representation function of a quadratic form, and Ψ = (ψ1, …, ψt) is a system of linear forms of finite complexity. When all the functions Fi are equal to the von Mangoldt function, we recover a result of Green and Tao, while when they are all representation functions of quadratic forms, we recover a result of Matthiesen. Our formulae imply asymptotics for some polynomial patterns in the primes. For instance, they describe the asymptotic behaviour of the number of k-term arithmetic progressions of primes whose common difference is a sum of two squares.The paper combines ingredients from the work of Green and Tao on linear equations in primes and that of Matthiesen on linear correlations amongst integers represented by a quadratic form. To make the von Mangoldt function compatible with the representation function of a quadratic form, we provide a new pseudorandom majorant for both – an average of the known majorants for each of the functions – and prove that it has the required pseudorandomness properties.
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2

Kunik, Matthias, and Lutz G. Lucht. "Power series with the von Mangoldt function." Functiones et Approximatio Commentarii Mathematici 47, no. 1 (September 2012): 15–33. http://dx.doi.org/10.7169/facm/2012.47.1.2.

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3

EISNER, TANJA. "Nilsystems and ergodic averages along primes." Ergodic Theory and Dynamical Systems 40, no. 10 (April 11, 2019): 2769–77. http://dx.doi.org/10.1017/etds.2019.27.

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A celebrated result by Bourgain and Wierdl states that ergodic averages along primes converge almost everywhere for $L^{p}$-functions, $p>1$, with a polynomial version by Wierdl and Nair. Using an anti-correlation result for the von Mangoldt function due to Green and Tao, we observe everywhere convergence of such averages for nilsystems and continuous functions.
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4

Fujii, Akio. "Eigenvalues of the Laplace-Beltrami operator and the von-Mangoldt function." Proceedings of the Japan Academy, Series A, Mathematical Sciences 69, no. 5 (1993): 125–30. http://dx.doi.org/10.3792/pjaa.69.125.

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5

Hast, Daniel Rayor, and Vlad Matei. "Higher Moments of Arithmetic Functions in Short Intervals: A Geometric Perspective." International Mathematics Research Notices 2019, no. 21 (January 29, 2018): 6554–84. http://dx.doi.org/10.1093/imrn/rnx310.

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Abstract We study the geometry associated to the distribution of certain arithmetic functions, including the von Mangoldt function and the Möbius function, in short intervals of polynomials over a finite field $\mathbb{F}_{q}$. Using the Grothendieck–Lefschetz trace formula, we reinterpret each moment of these distributions as a point-counting problem on a highly singular complete intersection variety. We compute part of the ℓ-adic cohomology of these varieties, corresponding to an asymptotic bound on each moment for fixed degree n in the limit as $q \to \infty $. The results of this paper can be viewed as a geometric explanation for asymptotic results that can be proved using analytic number theory over function fields.
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6

BANKS, WILLIAM D., JOHN B. FRIEDLANDER, MOUBARIZ Z. GARAEV, and IGOR E. SHPARLINSKI. "EXPONENTIAL AND CHARACTER SUMS WITH MERSENNE NUMBERS." Journal of the Australian Mathematical Society 92, no. 1 (February 2012): 1–13. http://dx.doi.org/10.1017/s1446788712000109.

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AbstractWe give new bounds on sums of the form ∑ n≤NΛ(n)exp (2πiagn/m) and ∑ n≤NΛ(n)χ(gn+a), where Λ is the von Mangoldt function, m is a natural number, a and g are integers coprime to m, and χ is a multiplicative character modulo m. In particular, our results yield bounds on the sums ∑ p≤Nexp (2πiaMp/m) and ∑ p≤Nχ(Mp) with Mersenne numbers Mp=2p−1, where p is prime.
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7

Geštautas, Andrius, and Antanas Laurinčikas. "On Universality of Some Beurling Zeta-Functions." Axioms 13, no. 3 (February 23, 2024): 145. http://dx.doi.org/10.3390/axioms13030145.

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Let P be the set of generalized prime numbers, and ζP(s), s=σ+it, denote the Beurling zeta-function associated with P. In the paper, we consider the approximation of analytic functions by using shifts ζP(s+iτ), τ∈R. We assume the classical axioms for the number of generalized integers and the mean of the generalized von Mangoldt function, the linear independence of the set {logp:p∈P}, and the existence of a bounded mean square for ζP(s). Under the above hypotheses, we obtain the universality of the function ζP(s). This means that the set of shifts ζP(s+iτ) approximating a given analytic function defined on a certain strip σ^<σ<1 has a positive lower density. This result opens a new chapter in the theory of Beurling zeta functions. Moreover, it supports the Linnik–Ibragimov conjecture on the universality of Dirichlet series.For the proof, a probabilistic approach is applied.
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8

Berra-Montiel, Jasel, and Alberto Molgado. "Polymeric quantum mechanics and the zeros of the Riemann zeta function." International Journal of Geometric Methods in Modern Physics 15, no. 06 (May 8, 2018): 1850095. http://dx.doi.org/10.1142/s0219887818500950.

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We analyze the Berry–Keating model and the Sierra and Rodríguez-Laguna Hamiltonian within the polymeric quantization formalism. By using the polymer representation, we obtain for both models, the associated polymeric quantum Hamiltonians and the corresponding stationary wave functions. The self-adjointness condition provides a proper domain for the Hamiltonian operator and the energy spectrum, which turned out to be dependent on an introduced scale parameter. By performing a counting of semiclassical states, we prove that the polymer representation reproduces the smooth part of the Riemann–von Mangoldt formula, and also introduces a correction depending on the energy and the scale parameter. This may shed some light on the understanding of the fluctuation behavior of the zeros of the Riemann function from a purely quantum point of view.
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9

Pilatte, Cédric. "A solution to the Erdős–Sárközy–Sós problem on asymptotic Sidon bases of order 3." Compositio Mathematica 160, no. 6 (May 10, 2024): 1418–32. http://dx.doi.org/10.1112/s0010437x24007140.

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A set $S\subset {\mathbb {N}}$ is a Sidon set if all pairwise sums $s_1+s_2$ (for $s_1, s_2\in S$ , $s_1\leqslant s_2$ ) are distinct. A set $S\subset {\mathbb {N}}$ is an asymptotic basis of order 3 if every sufficiently large integer $n$ can be written as the sum of three elements of $S$ . In 1993, Erdős, Sárközy and Sós asked whether there exists a set $S$ with both properties. We answer this question in the affirmative. Our proof relies on a deep result of Sawin on the $\mathbb {F}_q[t]$ -analogue of Montgomery's conjecture for convolutions of the von Mangoldt function.
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Jiang, Yujiao, and Guangshi Lü. "Exponential sums formed with the von Mangoldt function and Fourier coefficients of $${ GL}(m)$$ G L ( m ) automorphic forms." Monatshefte für Mathematik 184, no. 4 (May 27, 2017): 539–61. http://dx.doi.org/10.1007/s00605-017-1068-4.

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Дисертації з теми "Von Mangoldt function"

1

MATSUMOTO, KOHJI, and SHIGEKI EGAMI. "CONVOLUTIONS OF THE VON MANGOLDT FUNCTION AND RELATED DIRICHLET SERIES." World Scientific Publishing, 2007. http://hdl.handle.net/2237/20354.

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Gozé, Vincent. "Une version effective du théorème des nombres premiers de Wen Chao Lu." Electronic Thesis or Diss., Littoral, 2024. http://www.theses.fr/2024DUNK0725.

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Анотація:
Le théorème des nombres premiers, démontré pour la première fois en 1896 à l'aide de l'analyse complexe, donne le terme principal pour la répartition asymptotique des nombres premiers. Ce n'est qu'en 1949 que la première démonstration dite "élémentaire" fut publiée : elle repose uniquement sur l'analyse réelle. En 1999, Wen Chao Lu a obtenu de manière élémentaire un terme d'erreur dans le théorème des nombres premiers très proche de celui fourni par la région sans zéro de la fonction zêta de Riemann donnée par La Vallée Poussin à la fin du XIXe siècle. Dans cette thèse, nous rendons explicite le résultat de Lu afin d'une part, de donner le meilleur terme d'erreur obtenu par méthodes élémentaires à ce jour, et d'autre part, de déterminer les limites de sa méthode
The prime number theorem, first proved in 1896 using complex analysis, gives the main term for the asymptotic distribution of prime numbers. It was not until 1949 that the first so-called "elementary" proof was published: it rests strictly on real analysis.In 1999, Wen Chao Lu obtained by an elementary method an error term in the prime number theorem very close to the one provided by the zero-free region of the Riemann zeta function given by La Vallée Poussin at the end of the 19th century. In this thesis, we make Lu's result explicit in order, firstly, to give the best error term obtained by elementary methods so far, and secondly, to explore the limits of his method
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Тези доповідей конференцій з теми "Von Mangoldt function"

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EGAMI, SHIGEKI, and KOHJI MATSUMOTO. "CONVOLUTIONS OF THE VON MANGOLDT FUNCTION AND RELATED DIRICHLET SERIES." In Proceedings of the 4th China-Japan Seminar. WORLD SCIENTIFIC, 2007. http://dx.doi.org/10.1142/9789812770134_0001.

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