Relevant bibliographies by topics / Frobenius trace

Academic literature on the topic 'Frobenius trace'

Author: Grafiati
Published: 10 December 2022
Last updated: 28 January 2023

Create a spot-on reference in APA, MLA, Chicago, Harvard, and other styles

Select a source type:

Contents

Consult the lists of relevant articles, books, theses, conference reports, and other scholarly sources on the topic 'Frobenius trace.'

Next to every source in the list of references, there is an 'Add to bibliography' button. Press on it, and we will generate automatically the bibliographic reference to the chosen work in the citation style you need: APA, MLA, Harvard, Chicago, Vancouver, etc.

You can also download the full text of the academic publication as pdf and read online its abstract whenever available in the metadata.

Journal articles on the topic "Frobenius trace"

1

Bae, Sunghan. "Statistics of traces of high powers of the Frobenius for biquadratic function fields over finite fields." International Journal of Number Theory 15, no. 08 (August 19, 2019): 1675–91. http://dx.doi.org/10.1142/s1793042119500933.

Full text
Abstract:
We investigate statistics of trace of high powers of the Frobenius class for biquadratic function fields over finite fields, which generalizes the result of Lorenzo, Meleleo and Milione on the trace of the Frobenius class for biquadratic covers of the projective line. Then we compare our result with Meisner’s result on the expected value of high powers of trace of Frobenius of biquadratic curves.
APA, Harvard, Vancouver, ISO, and other styles
2

CAENEPEEL, S., and T. GUÉDÉNON. "FULLY BOUNDED NOETHERIAN RINGS AND FROBENIUS EXTENSIONS." Journal of Algebra and Its Applications 06, no. 02 (April 2007): 189–206. http://dx.doi.org/10.1142/s0219498807002107.

Full text
Abstract:
Let i: A → R be a ring morphism, and χ: R → A a right R-linear map with χ(χ(r)s) = χ(rs) and χ(1R) = 1A. If R is a Frobenius A-ring, then we can define a trace map tr: A → AR. If there exists an element of trace 1 in A, then A is right FBN if and only if AR is right FBN and A is right noetherian. The result can be generalized to the case where R is an I-Frobenius A-ring. We recover results of García and del Río, and Dǎscǎlescu, Kelarev and Torrecillas on actions of group and Hopf algebras on FBN rings as special cases. We also obtain applications to extensions of Frobenius algebras, and to Frobenius corings with a grouplike element.
APA, Harvard, Vancouver, ISO, and other styles
3

Yun, Zhiwei, and Christelle Vincent. "Galois representations attached to moments of Kloosterman sums and conjectures of Evans." Compositio Mathematica 151, no. 1 (October 7, 2014): 68–120. http://dx.doi.org/10.1112/s0010437x14007593.

Full text
Abstract:
AbstractKloosterman sums for a finite field $\mathbb{F}_{p}$ arise as Frobenius trace functions of certain local systems defined over $\mathbb{G}_{m,\mathbb{F}_{p}}$. The moments of Kloosterman sums calculate the Frobenius traces on the cohomology of tensor powers (or symmetric powers, exterior powers, etc.) of these local systems. We show that when $p$ ranges over all primes, the moments of the corresponding Kloosterman sums for $\mathbb{F}_{p}$ arise as Frobenius traces on a continuous $\ell$-adic representation of $\text{Gal}(\overline{\mathbb{Q}}/\mathbb{Q})$ that comes from geometry. We also give bounds on the ramification of these Galois representations. All of this is done in the generality of Kloosterman sheaves attached to reductive groups introduced by Heinloth, Ngô and Yun [Ann. of Math. (2) 177 (2013), 241–310]. As an application, we give proofs of conjectures of Evans [Proc. Amer. Math. Soc. 138 (2010), 517–531; Israel J. Math. 175 (2010), 349–362] expressing the seventh and eighth symmetric power moments of the classical Kloosterman sum in terms of Fourier coefficients of explicit modular forms. The proof for the eighth symmetric power moment conjecture relies on the computation done in Appendix B by C. Vincent.
APA, Harvard, Vancouver, ISO, and other styles
4

Kurniadi, Edi. "KILLING FORM ALJABAR LIE FROBENIUS BERDIMENSI ≤4 UNTUK MENENTUKAN KESEMISEDERHANAANNYA." EduMatSains : Jurnal Pendidikan, Matematika dan Sains 6, no. 1 (July 1, 2021): 101–10. http://dx.doi.org/10.33541/edumatsains.v6i1.2999.

Full text
Abstract:
We study the notion of the Killing form for Frobenius Lie algebras of dimension . The Killing form is a symmetric bilinear form on a finite dimensional Lie algebra over a field defined by where is denoted the trace and is an adjoint representation of . A Lie algebras is said to be semisimple if it has the nondegenerate Killing form. The research aims to consider the criterion for semisimplicity of Frobenius Lie algebras of dimension by using the Killing form. The results show that each Frobenius Lie algebra of dimension and is not semisimple since the the Killing form is degenerate or in other words, a determinant of a representation matrix of the Killing form is equal to zero. For the future research, it is still an open problem to consider the general formulas of the Killing form for higher dimensional Frobenius Lie algebra whether degenerate or nondegenerate such that the semisimplicity of a Lie algebra can be considered. We conjecture that each finite dimensional real Frobenius Lie algebra is not semisimple.
APA, Harvard, Vancouver, ISO, and other styles
5

Chávez, Ángel, and George Todd. "Supercharacters and mixed moments of Kloosterman sums." International Journal of Number Theory 14, no. 04 (May 2018): 1023–32. http://dx.doi.org/10.1142/s1793042118500616.

Full text
Abstract:
Recent work has realized Kloosterman sums as supercharacter values of a supercharacter theory on [Formula: see text]. We use this realization to express fourth degree mixed power moments of Kloosterman sums in terms of the trace of Frobenius of a certain elliptic curve.
APA, Harvard, Vancouver, ISO, and other styles
6

Tanaka, Hiromu. "The trace map of Frobenius and extending sections for threefolds." Michigan Mathematical Journal 64, no. 2 (June 2015): 227–61. http://dx.doi.org/10.1307/mmj/1434731922.

Full text
APA, Harvard, Vancouver, ISO, and other styles
7

HUMPHRIES, PETER. "ON THE MERTENS CONJECTURE FOR ELLIPTIC CURVES OVER FINITE FIELDS." Bulletin of the Australian Mathematical Society 89, no. 1 (February 28, 2013): 19–32. http://dx.doi.org/10.1017/s0004972712001116.

Full text
Abstract:
AbstractWe introduce an analogue of the Mertens conjecture for elliptic curves over finite fields. Using a result of Waterhouse, we classify the isogeny classes of elliptic curves for which this conjecture holds in terms of the size of the finite field and the trace of the Frobenius endomorphism acting on the curve.
APA, Harvard, Vancouver, ISO, and other styles
8

SADEK, MOHAMMAD. "FORMAL GROUPS AND INVARIANT DIFFERENTIALS OF ELLIPTIC CURVES." Bulletin of the Australian Mathematical Society 92, no. 1 (May 4, 2015): 44–51. http://dx.doi.org/10.1017/s0004972715000295.

Full text
Abstract:
In this paper, we find a power series expansion of the invariant differential ${\it\omega}_{E}$ of an elliptic curve $E$ defined over $\mathbb{Q}$, where $E$ is described by certain families of Weierstrass equations. In addition, we derive several congruence relations satisfied by the trace of the Frobenius endomorphism of $E$.
APA, Harvard, Vancouver, ISO, and other styles
9

Ishii, Noburo. "Trace of Frobenius endomorphism of an elliptic curve with complex multiplication." Bulletin of the Australian Mathematical Society 70, no. 1 (August 2004): 125–42. http://dx.doi.org/10.1017/s0004972700035875.

Full text
Abstract:
Let E be an elliptic curve with complex multiplication by R, where R is an order of discriminant D < −4 of an imaginary quadratic field K. If a prime number p is decomposed completely in the ring class field associated with R, then E has good reduction at a prime ideal p of K dividing p and there exist positive integers u and υ such that 4p = u2 – Du;2. It is well known that the absolute value of the trace ap of the Frobenius endomorphism of the reduction of E modulo p is equal to u. We determine whether ap = u or ap = −u in the case where the class number of R is 2 or 3 and D is divisible by 3, 4 or 5.
APA, Harvard, Vancouver, ISO, and other styles
10

Kadison, Lars, and Burkhard Külshammer. "Depth Two, Normality, and a Trace Ideal Condition for Frobenius Extensions." Communications in Algebra 34, no. 9 (September 2006): 3103–22. http://dx.doi.org/10.1080/00927870600650291.

Full text
APA, Harvard, Vancouver, ISO, and other styles
More sources

Dissertations / Theses on the topic "Frobenius trace"

1

Ekdahl, Filipsson Fabian. "Trajectory and Pulse Optimization for Active Towed Array Sonar using MPC and Information Measures." Thesis, Uppsala universitet, Avdelningen för systemteknik, 2020. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-420532.

Full text
Abstract:
In underwater tracking and surveillance, the active towed array sonar presents a way of discovering and tracking adversarial submerged targets that try to stay hidden. The configuration consist of listening and emitting hydrophones towed behind a ship. Moreover, it has inherent limitations, and the characteristics of sound in the ocean are complex. By varying the pulse form emitted and the trajectory of the ship the measurement accuracy may be improved. This type of optimization constitutes a sensor management problem. In this thesis, a model of the tracking scenario has been constructed derived from Cramér-Rao bound analyses. A model predictive control approach together with information measures have been used to optimize a filter's estimated state of the target. For the simulations, the MATLAB environment has been used. Different combinations of decision horizons, information measures and variations of the Kalman filter have been studied. It has been found that the accuracy of the Extended Kalman filter is too low to give consistent results given the studied information measures. However, the Unscented Kalman filter is sufficient for this purpose.
APA, Harvard, Vancouver, ISO, and other styles
2

Tenzler, Julian [Verfasser], and Michael [Akademischer Betreuer] Dettweiler. "Fourier-Deligne transformation of perverse sheaves and the change of Frobenius traces under the Katz algorithm / Julian Tenzler ; Betreuer: Michael Dettweiler." Bayreuth : Universität Bayreuth, 2020. http://d-nb.info/1205804803/34.

Full text
APA, Harvard, Vancouver, ISO, and other styles
3

Chiriac, Liubomir. "Special Frobenius Traces in Galois Representations." Thesis, 2015. https://thesis.library.caltech.edu/8942/1/Chiriac_Thesis.pdf.

Full text
Abstract:

This thesis studies Frobenius traces in Galois representations from two different directions. In the first problem we explore how often they vanish in Artin-type representations. We give an upper bound for the density of the set of vanishing Frobenius traces in terms of the multiplicities of the irreducible components of the adjoint representation. Towards that, we construct an infinite family of representations of finite groups with an irreducible adjoint action.

In the second problem we partially extend for Hilbert modular forms a result of Coleman and Edixhoven that the Hecke eigenvalues ap of classical elliptical modular newforms f of weight 2 are never extremal, i.e., ap is strictly less than 2[square root]p. The generalization currently applies only to prime ideals p of degree one, though we expect it to hold for p of any odd degree. However, an even degree prime can be extremal for f. We prove our result in each of the following instances: when one can move to a Shimura curve defined by a quaternion algebra, when f is a CM form, when the crystalline Frobenius is semi-simple, and when the strong Tate conjecture holds for a product of two Hilbert modular surfaces (or quaternionic Shimura surfaces) over a finite field.

APA, Harvard, Vancouver, ISO, and other styles

Book chapters on the topic "Frobenius trace"

1

Gaitsgory, Dennis, and Jacob Lurie. "Computing the Trace of Frobenius." In Weil's Conjecture for Function Fields, 204–38. Princeton University Press, 2019. http://dx.doi.org/10.23943/princeton/9780691182148.003.0004.

Full text
Abstract:
This chapter aims to compute the trace Tr(Frob-1 ¦H* (BunG(X);Zℓ)), where ℓ is a prime number which is invertible in F q. It follows the strategy outlined in Chapter 1. If X is an algebraic curve over the field C of complex numbers and G is a smooth affine group scheme over X whose fibers are semisimple and simply connected, then Theorem 1.5.4.10 (and Example 1.5.4.15) supply a quasi-isomorphism whose right-hand side is the continuous tensor product of Construction 1.5.4.8. The remainder of this chapter is devoted to explaining how Theorem 4.1.2.1 can be used to compute the trace of the arithmetic Frobenius automorphism on the ℓ-adic cohomology of BunG(X).
APA, Harvard, Vancouver, ISO, and other styles
2

"Computing the Trace of Frobenius." In Weil's Conjecture for Function Fields, 204–38. Princeton University Press, 2019. http://dx.doi.org/10.2307/j.ctv4v32qc.6.

Full text
APA, Harvard, Vancouver, ISO, and other styles
3

"Chapter Four. Computing the Trace of Frobenius." In Weil's Conjecture for Function Fields, 204–38. Princeton University Press, 2019. http://dx.doi.org/10.1515/9780691184432-004.

Full text
APA, Harvard, Vancouver, ISO, and other styles
4

Reutenauer, Christophe. "Markoff Numbers." In From Christoffel Words to Markoff Numbers, 21–28. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198827542.003.0004.

Full text
Abstract:
The Markoff equation is the diophantine equation x2 +y2 +z2 = 3xyz. A solution is called a Markoff triple. The main result in this chapter is a bijection between lower Christoffel words and Markoff triples. The bijection uses several ingredients: a special representation of the free monoid into SL2(N), the so-called Fricke relations, which relate the traces of two matrices in SL2, their product and their commutator (an equation reminiscent of the Markoff equation, as noted first by Harvey Cohn). Another lemma describes the socalled Markoff moves: they relate Markoff triples each to another. The chapter ends with a statement of the famous Frobenius conjecture: it asks whether the parametrization of Markoff numbers (that is, components of a Markoff triple), which is surjective by the theorem, is also injective.
APA, Harvard, Vancouver, ISO, and other styles

Conference papers on the topic "Frobenius trace"

1

Greferath, Marcus, and Alexandr Nechaev. "Generalized Frobenius extensions of finite rings and trace functions." In 2010 IEEE Information Theory Workshop (ITW 2010). IEEE, 2010. http://dx.doi.org/10.1109/cig.2010.5592917.

Full text
APA, Harvard, Vancouver, ISO, and other styles
2

Ramani, Keval S., and Chinedum E. Okwudire. "Two-Stage Robust Tracking Controller for Linear Systems With Known Uncertainty Using Filtered Basis Functions." In ASME 2020 Dynamic Systems and Control Conference. American Society of Mechanical Engineers, 2020. http://dx.doi.org/10.1115/dscc2020-3207.

Full text
Abstract:
Abstract There is growing interest in the use of the filtered basis functions (FBF) approach to track linear systems, especially nonminimum phase (NMP) plants, because of the distinct advantages it presents as compared to other popular methods in the literature. The FBF approach expresses the control input to the plant as a linear combination of basis functions. The basis functions are forward filtered through the plant dynamics and the coefficients of the linear combination are selected such that the tracking error is minimized. This paper proposes a two-stage robust filtered basis functions approach for tracking control of linear systems in the presence of known uncertainty. In the first stage, the nominal model for filtering the basis functions is selected such that a Frobenius norm metric which considers the known uncertainty is minimized. In the second stage, an optimal set of basis functions is selected such that the effect of uncertainty is minimized for the nominal model selected in the first stage. Experiments on a 3D printer, demonstrate up to 7 times improvement in tracking performance using the proposed method as compared to the standard FBF approach.
APA, Harvard, Vancouver, ISO, and other styles
3

Sardahi, Yousef, Yuan Yao, and Jian-Qiao Sun. "Multi-Objective Optimal Control of Under-Actuated Bogie System of High Speed Trains." In ASME 2016 Dynamic Systems and Control Conference. American Society of Mechanical Engineers, 2016. http://dx.doi.org/10.1115/dscc2016-9622.

Full text
Abstract:
Feedback controls are important to the improvement of dynamic performance of high-speed trains. However, designing an active control for these vehicles is a very challenging task because the control system is usually under-actuated and has to meet multiple conflicting objectives. Examples of conflicting objectives include designing a highly relative stable system while minimizing the control efforts or maximizing the capability of the system to reject external disturbances. In addition, the mathematical models of these systems are not completely controllable and observable. This paper studies multi-objective optimal design of feedback controls for a sub-system of high-speed trains, i.e. the bogie system. The bogie system can be decomposed such that the observable and controllable components of the model are used to stabilize the internal states and therefore the overall system. A linear mathematical model of the system is used in the design. The controllable and the observable states of the model are separated to form a state-feedback control to drive the internal modes and the whole system to stability. A multi-objective genetic algorithm is used to search for the feedback control gains to optimize three objectives: the Frobenius norm of the control law, relative stability and the disturbance rejection. The solutions of the multi-objective optimization provide various trade-offs among the objectives. Numerical simulations show that the proposed control designs can stabilize the system even at a high critical speed of 500 km/h.
APA, Harvard, Vancouver, ISO, and other styles
You might also be interested in the extended bibliographies on the topic 'Frobenius trace' for particular source types:
Journal articles
We offer discounts on all premium plans for authors whose works are included in thematic literature selections. Contact us to get a unique promo code!

To the bibliography