Seoyoung Kim

activity

20172026

most citedExplicit constructions of Diophantine tuples over finite fields

3 citations · 10 across the 11 of their papers we have counts for

collaborators

12 papers

math.CO2026

Multiplicative irreducibility of shifted multiplicative subgroups

Seoyoung Kim, Chi Hoi Yip, Semin Yoo

In a recent breakthrough, Kalmynin resolved conjectures of Lev--Sonn and Sárközy on additive decompositions of multiplicative subgroups of prime fields. In this paper, inspired by…

math.CO2025

$f$ -Diophantine sets over finite fields via quasi-random hypergraphs from multivariate polynomials

Seoyoung Kim, Chi Hoi Yip, Semin Yoo

We investigate $f$ -Diophantine sets over finite fields via new explicit constructions of families of quasi-random hypergraphs from multivariate polynomials. In particular, our cons…

math.CO2024

Paley-like quasi-random graphs arising from polynomials

Seoyoung Kim, Chi Hoi Yip, Semin Yoo

Paley graphs and Paley sum graphs are classical examples of quasi-random graphs. In this paper, we provide new constructions of families of quasi-random graphs that behave like Pal…

math.NT2024★ 3 cited

Explicit constructions of Diophantine tuples over finite fields

Seoyoung Kim, Chi Hoi Yip, Semin Yoo

A Diophantine $m$ -tuple over a finite field $F_{q}$ is a set ${a_{1}, \dots, a_{m}}$ of $m$ distinct elements in $F_{q}^{*}$ such that $a_{i} a_{j} + 1$ is a square in $…

math.NT2023★ 3 cited

Multiplicative structure of shifted multiplicative subgroups and its applications to Diophantine tuples

Seoyoung Kim, Chi Hoi Yip, Semin Yoo

In this paper, we investigate the multiplicative structure of a shifted multiplicative subgroup and its connections with additive combinatorics and the theory of Diophantine equati…

math.NT2022

$k$ -Diophantine $m$ -tuples in Finite Fields

Trajan Hammonds, Seoyoung Kim, Steven J. Miller +4

In this paper, we define a $k$ -Diophantine $m$ -tuple to be a set of $m$ positive integers such that the product of any $k$ distinct positive integers is one less than a perfect squ…

math.NT2021

From the Birch and Swinnerton-Dyer conjecture to Nagao's conjecture

Seoyoung Kim, M. Ram Murty

Let $E$ be an elliptic curve over $Q$ with discriminant $Δ_{E}$ . For primes $p$ of good reduction, let $N_{p}$ be the number of points modulo $p$ and write $N_{p} = p + 1 - a_{p}$ . In 1…

math.AG2020

Building bridges between Tate conjectures and arithmetic invariants

Victoria Cantoral-Farfan, Seoyoung Kim

In this paper, we clarify and build connections between various conjectures largely motivated by the works of Jean-Pierre Serre and John Tate. We closely study the Tate conjecture…

math.NT2019

Rank and Bias in Families of Hyperelliptic Curves via Nagao's Conjecture

Trajan Hammonds, Seoyoung Kim, Benjamin Logsdon +2

Let $X : y^{2} = f (x)$ be a hyperelliptic curve over $Q (T)$ of genus $g \geq 1$ . Assume that the jacobian of $X$ over $Q (T)$ has no subvariety de…

math.NT2018

Elliptic Fermat numbers and elliptic divisibility sequence

Seoyoung Kim, Alexandra Walsh

For a pair $(E, P)$ of an elliptic curve $E / Q$ and a nontorsion point $P \in E (Q)$ , the sequence of \emph{elliptic Fermat numbers} is defined by taking quotients of…

math.NT2017★ 1 cited

The Sato-Tate conjecture and Nagao's conjecture

Seoyoung Kim

Nagao's conjecture relates the rank of an elliptic surface to a limit formula arising from a weighted average of fibral Frobenius traces, and it is further generalized for smooth i…

math.NT2017★ 3 cited

The density of the terms in an elliptic divisibility sequence having a fixed G.C.D. with their index

Seoyoung Kim

Let $D = (D_{n})_{n \geq 1}$ be an elliptic divisibility sequence associated to the pair $(E, P)$ . For a fixed integer $k$ , we define $\mathscr{A}_{E,k}=\{n\geq 1 : \gcd(n,D_{…

Multiplicative irreducibility of shifted multiplicative subgroups

f-Diophantine sets over finite fields via quasi-random hypergraphs from multivariate polynomials

Paley-like quasi-random graphs arising from polynomials

Explicit constructions of Diophantine tuples over finite fields

Multiplicative structure of shifted multiplicative subgroups and its applications to Diophantine tuples

k-Diophantine m-tuples in Finite Fields

From the Birch and Swinnerton-Dyer conjecture to Nagao's conjecture

Building bridges between Tate conjectures and arithmetic invariants

Rank and Bias in Families of Hyperelliptic Curves via Nagao's Conjecture

Elliptic Fermat numbers and elliptic divisibility sequence

The Sato-Tate conjecture and Nagao's conjecture

The density of the terms in an elliptic divisibility sequence having a fixed G.C.D. with their index

$f$ -Diophantine sets over finite fields via quasi-random hypergraphs from multivariate polynomials

$k$ -Diophantine $m$ -tuples in Finite Fields