T. Hammonds

activity

20172026

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Showing 2019Show all

3 papers · 1 filter

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…

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

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

The Explicit Sato-Tate Conjecture For Primes In Arithmetic Progressions

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