T. Hammonds

collaborators

3 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.CO2019

Modified Erdős-Ginzburg-Ziv Constants for $(Z / n Z)^{2}$

Trajan Hammonds

For an abelian group $G$ and an integer $t > 0$ , the modified Erdős-Ginzburg-Ziv constant $s_{t}^{'} (G)$ is the smallest integer $ℓ$ such that any zero-sum sequence of length at leas…

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…

k-Diophantine m-tuples in Finite Fields

Modified Erdős-Ginzburg-Ziv Constants for (Z/nZ)2

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

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

Modified Erdős-Ginzburg-Ziv Constants for $(Z / n Z)^{2}$