arXiv subjects

WonTae Hwang

Publications and source records attributed to WonTae Hwang.

14 recordsLinked to original sources

arXiv2026

Frobenius Alexander quandles, knot colorings, and isogeny classes of abelian varieties over finite fields

We introduce the notion of Frobenius Alexander quandles associated with abelian varieties over finite fields, and study them from both knot-theoretic and arithmetic viewpoints. We determine exactly for which rational primes a knot admits a nonconstant coloring by these quandles, in terms of the resultant of its Alexander polynomial and the Frobenius characteristic polynomial of the abelian variety. This leads to the notion of persistent colorability and its characterization, as well as applications to fibered knots and knots of small genus. We also prove a rigidity result showing that the isomorphism class of a Frobenius Alexander quandle determines the similarity class of the Frobenius endomorphism on the corresponding torsion subgroup. As a consequence, one sufficiently large Frobenius Alexander quandle determines the characteristic polynomial of the Frobenius endomorphism, and hence, determines the isogeny class of the abelian variety over the given finite base field.

math.GT↗

arXiv2025

The Frobenius problem for Numerical Semigroups generated by binomial coefficients

The greatest integer that does not belong to a numerical semigroup $S$ is called the Frobenius number of $S$, and finding the Frobenius number is called the Frobenius problem. In this paper, we solve the Frobenius problem for the numerical semigroups generated by binomial coefficients. As applications, we provide some nontrivial identities among binomial coefficients, and we also connect the main results to the theory of $(s,s+1,s+p)$-core partitions of integers.

math.NT↗

arXiv2025

Non-Jordaness of the automorphism group of the zero-divisor graph of a matrix ring over number rings

We provide a construction of the induced subgraphs of the zero-divisor graph of $M_2(R)$ for the ring $R$ of algebraic integers of some number fields that are neither complete nor connected, and study the structure of the induced subgraphs explicitly. As an application, we prove that the automorphism group of the zero-divisor graph of $M_2(R)$ is not a Jordan group.

math.CO↗

arXiv2022

Jordan constants of abelian surfaces over finite fields

We compute the exact values of the Jordan constants of abelian surfaces over finite fields.

math.GR↗

arXiv2021

On the automorphism groups of simple polarized abelian fourfolds over finite fields and Jordan constants

We give a classification of maximal elements of the set of finite groups that can be realized as the full automorphism groups of simple polarized abelian fourfolds over finite fields. As an application, we compute the Jordan constants of the automorphism groups of simple abelian fourfolds over finite fields.

math.NT↗

arXiv2020

A classification of the automorphism groups of polarized abelian threefolds over finite fields

We give a classification of maximal elements of the set of finite groups that can be realized as the automorphism groups of polarized abelian threefolds over finite fields.

math.NT↗

arXiv2020

Jordan constants of quaternion algebras over number fields and simple abelian surfaces over fields of positive characteristic

We compute and provide a detailed description on the Jordan constants of the multiplicative subgroup of quaternion algebras over number fields of small degree. As an application, we determine the Jordan constants of the multiplicative subgroup of the endomorphism algebras of simple abelian surfaces over fields of positive characteristic.

math.GR↗

arXiv2020

Counting the number of the twists of certain polarized abelian varieties

We count the number of isomorphism classes of degree $d$-twists of some polarized abelian varieties over finite fields of odd prime dimension. This can be seen as a higher dimensional analogue of the counting problem for elliptic curves case.

math.NT↗

arXiv2020

Absolutely simple polarized abelian varieties of odd Sophie Germain prime dimension over finite fields with maximal automorphism groups

For each Sophie Germain prime $g \geq 5,$ we construct an absolutely simple polarized abelian variety of dimension $g$ over a finite field, whose automorphism group is a cyclic group of order $4g+2$. We also provide a description on the asymptotic behavior of prime numbers that are related to our construction.

math.NT↗

arXiv2019

On the integer part of the reciprocal of the Riemann zeta function tail at certain rational numbers in the critical strip

We prove that the integer part of the reciprocal of the tail of $ζ(s)$ at a rational number $s=\frac{1}{p}$ for any integer with $p \geq 5$ or $s=\frac{2}{p}$ for any odd integer with $p \geq 5$ can be described essentially as the integer part of an explicit quantity corresponding to it. To deal with the case when $s=\frac{2}{p},$ we use a result on the finiteness of integral points of certain curves over $\mathbb{Q}$.

math.NT↗

arXiv2019

Automorphism groups of simple polarized abelian varieties of odd prime dimension over finite fields

We prove that the automorphism groups of simple polarized abelian varieties of odd prime dimension over finite fields are cyclic, and give a complete list of finite groups that can be realized as such automorphism groups.

math.NT↗

arXiv2018

On a generalized $k$-FL sequence and its applications

We introduce a generalized $k$-FL sequence and special kind of pairs of real numbers that are related to it, and give an application on the integral solutions of a certain equation using those pairs. Also, we associate skew circulant and circulant matrices to each generalized $k$-FL sequence, and study the determinantal variety of those matrices as an application.

math.NT↗

arXiv2018

On a classification of the automorphism groups of polarized abelian surfaces over finite fields

We give a classification of maximal elements of the set of finite groups that can be realized as the full automorphism groups of polarized abelian surfaces over finite fields.

math.NT↗

arXiv2017

A reciprocal sum related to the Riemann zeta function at s=6

We introduce an explicit formula for a reciprocal sum related to the Riemann zeta function at s=6, and pose one question related to a computational formula for larger values of s.

math.NT↗