T. Hammonds

activity

20172026

collaborators

7 papers

math.RT2026

Relative Character Asymptotics Beyond Stability for $PGL_{2} \times GL_{1}$

Trajan Hammonds

The asymptotics of relative characters for real Lie groups were studied for representations $(π, σ)$ arising from Gan-Gross-Prasad pairs $(G, H)$ by Nelson and Venkatesh. They succe…

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

The completed standard $L$ -function of modular forms on $G_{2}$

Fatma Çiçek, Giuliana Davidoff, Sarah Dijols +3

The goal of this paper is to provide a complete and refined study of the standard $L$ -functions $L (π, Std, s)$ for certain non-generic cuspidal automorphic representat…

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…

math.NT2019

The Explicit Sato-Tate Conjecture For Primes In Arithmetic Progressions

Trajan Hammonds, Casimir Kothari, Noah Luntzlara +3

Let $τ (n)$ be Ramanujan's tau function, defined by the discriminant modular form \[ Δ(z) = q\prod_{j=1}^{\infty}(1-q^{j})^{24}\ =\ \sum_{n=1}^{\infty}τ(n) q^n \,,q=e^{2πi z} \] (th…

math.NT2017

Counting Roots of Polynomials over $Z / p^{2} Z$

Trajan Hammonds, Jeremy Johnson, Angela Patini +1

Until recently, the only known method of finding the roots of polynomials over prime power rings, other than fields, was brute force. One reason for this is the lack of a division…

Relative Character Asymptotics Beyond Stability for PGL2​×GL1​

k-Diophantine m-tuples in Finite Fields

The completed standard L-function of modular forms on G2​

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