Article
Mathematics
Jonas Bergstrom, Valentijn Karemaker, Stefano Marseglia
Summary: We describe the polarizations for abelian varieties over a finite field in a fixed isogeny class corresponding to a squarefree Weil polynomial, when one variety in the class can be lifted to characteristic zero with an isomorphism of endomorphism rings induced by the reduction morphism.
INTERNATIONAL MATHEMATICS RESEARCH NOTICES
(2023)
Article
Mathematics, Applied
WonTae Hwang
Summary: The study provides a classification of maximal elements of finite groups that can be realized as the full automorphism groups of polarized abelian surfaces over finite fields.
FINITE FIELDS AND THEIR APPLICATIONS
(2021)
Correction
Mathematics, Applied
Alejandro J. Giangreco-Maidana
Summary: This paper presents the correct statement of main Theorem 2.1.
FINITE FIELDS AND THEIR APPLICATIONS
(2021)
Article
Mathematics
Davesh Maulik, Ananth N. Shankar, Yunqing Tang
Summary: This passage discusses the properties of a non-isotrivial ordinary abelian surface A over a global function field. When A satisfies certain conditions, it is proven that A is isogenous to the product of two elliptic curves in infinitely many places modulo.
COMPOSITIO MATHEMATICA
(2022)
Article
Mathematics
George Boxer, Frank Calegari, Toby Gee, Vincent Pilloni
Summary: This study demonstrates that abelian surfaces over totally real fields may be potentially modular, leading to the expected meromorphic continuation and functional equations of their Hasse-Weil zeta functions. Additionally, the modularity of numerous abelian surfaces over Q with EndCA=Z is shown. Furthermore, modularity and potential modularity results for genus one curves over (not necessarily CM) quadratic extensions of totally real fields are deduced.
PUBLICATIONS MATHEMATIQUES DE L IHES
(2021)
Article
Mathematics
Valerio Dose, Guido Lido, Pietro Mercuri, Claudio Stirpe
Summary: We describe an algorithm to compute the number of points over finite fields on a broad class of modular curves. We applied our algorithm to more than ten thousand curves and found over one hundred record-breaking curves.
JOURNAL OF ALGEBRA
(2023)
Article
Mathematics
Nicole R. Looper, Joseph H. Silverman
Summary: Under certain conditions, we prove the existence of a lower bound for the height of points on the abelian surface A. This is of significant importance for researchers in the field of function field theory and related areas.
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY
(2023)
Article
Mathematics, Applied
Jianying Rong, Fengwei Li, Ting Li
Summary: This paper constructs two classes of linear codes over Fq and investigates their weight distributions by calculating two classes of special exponential sums.
Article
Mathematics, Applied
Xiaoer Qin, Li Yan
Summary: Constructing permutation polynomials in finite fields is a popular topic. This paper investigates the construction of permutation polynomials over F-q3, using the AGW criterion and piecewise method. Several classes of permutation polynomials of the form (x(q2) + x(q) + x + delta)(q3-1/d) +1 + L(x), where d = 2, 3, 4, 6 and L(x) is a linearized polynomial over F-q, are constructed.
Article
Mathematics
WonTae Hwang
Summary: This paper computes and provides a detailed description of the Jordan constants of the multiplicative subgroup of quaternion algebras over number fields of small degree. As an application, it determines the Jordan constants of the multiplicative subgroup of the endomorphism algebras of simple abelian surfaces over fields of positive characteristic.
MATHEMATISCHE NACHRICHTEN
(2022)
Article
Computer Science, Theory & Methods
Song Tian
Summary: We propose a new method to solve the elliptic curve discrete logarithm problem over cubic extension fields F-q(3). The method applies an F-q-rational (l, l, l)-isogeny from the Weil restriction of the elliptic curve under consideration with respect to F-q(3) /F-q to the Jacobian variety of a genus three curve over F-q, and then solves the problem in the Jacobian via index-calculus attacks. Although this method does not use covering maps in the construction of the desired homomorphism, it can be considered a kind of cover attack in a sense. As a result, it is possible to solve the discrete logarithm problem in some elliptic curve groups of prime order over F-q(3) in a time of (O) over tilde (q).
JOURNAL OF CRYPTOLOGY
(2023)
Article
Chemistry, Physical
Jack Broad, Simon Preston, Richard J. Wheatley, Richard S. Graham
Summary: This paper outlines a strategy to reduce the number of training points required to model intermolecular potentials using Gaussian processes, without compromising accuracy. By using an asymptotic function and learning the crossover distance from training data, the technique successfully reduces the number of training points by up to 49% compared to previous sequential learning methods. The approach can be easily applied to other statistical prediction or modeling problems.
JOURNAL OF CHEMICAL PHYSICS
(2021)
Article
Mathematics, Applied
WonTae Hwang, Bo-Hae Im, Hansol Kim
Summary: We provide a classification of maximal elements of the automorphism groups of polarized abelian threefolds over finite fields.
FINITE FIELDS AND THEIR APPLICATIONS
(2022)
Article
Mathematics, Applied
Yucong He, Sihem Mesnager, Nian Li, Lisha Wang, Xiangyong Zeng
Summary: This paper introduces the applications of linear codes with few weights in various fields and proposes a new defining set. By using quadratic Gauss sums over finite fields, the parameters and weight distributions of the generated linear codes are fully determined. Additionally, two classes of optimal two-weight codes meeting the Griesmer bound are obtained from the constructions.
FINITE FIELDS AND THEIR APPLICATIONS
(2023)
Article
Mathematics
Alexandra Kuznetsova
Summary: This article proves that the group of automorphisms of any quasi-projective surface Sin in finite characteristic has the p-Jordan property.
JOURNAL OF ALGEBRA
(2022)
