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

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8 papers · 1 filter

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.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_{…

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

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

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