Seoyoung Kim

activity

20172022

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

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

collaborators

5 papers

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★ 3 cited

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