Steven J. Miller

activity

20192026

collaborators

6 papers

math.NT2026

Product and Quotient Set Dominance in Finite Groups

Yuval Amit, Lucas Chen, Christopher Housholder +5

A classic problem in additive number theory asks whether a given subset of integers has more sums or differences. This inquiry naturally extends to finite groups, where one compare…

math.AG2026

The Bias Conjecture for One-Parameter, Non-Isotrivial Elliptic Curve Families

Lucas Chen, Joshua Im, Steven J. Miller +1

We investigate Miller's bias conjecture for general one-parameter families of elliptic curves over $Q$ with non-constant $j$ -invariants. Utilizing methods developed by Mic…

math.NT2026

Bounding The Number of Zeros Near the Central Point in Families of Cuspidal Newforms

Lucas Chen, Christopher Housholder, Joshua Khan +2

We study low-lying zeros in families of even holomorphic cuspidal newforms of fixed weight and prime level, with particular emphasis on the number of forms having a zero in a presc…

math.NT2026

On the Existence of Hyperelliptic Curves over $Q (T)$ with Certain Jacobian Ranks

Lucas Chen, Joshua Im, Steven J. Miller +1

Let $y^{2} = f (x, T)$ be a hyperelliptic curve of genus $g \geq 1$ , defined over $Q (T)$ . We prove the existence of infinitely many imaginary hyperelliptic curves with a fixed…

math.NT2024

Lower Order Biases in Moment Expansions of One Parameter Families of Elliptic Curves

Timothy Cheek, Pico Gilman, Kareem Jaber +3

For a fixed elliptic curve $E$ without complex multiplication, $a_{p} := p + 1 - # E (F_{p})$ is $O (p)$ and $a_{p} /2 p$ converges to a semicircular distribution. Miche…

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…

Product and Quotient Set Dominance in Finite Groups

The Bias Conjecture for One-Parameter, Non-Isotrivial Elliptic Curve Families

Bounding The Number of Zeros Near the Central Point in Families of Cuspidal Newforms

On the Existence of Hyperelliptic Curves over Q(T) with Certain Jacobian Ranks

Lower Order Biases in Moment Expansions of One Parameter Families of Elliptic Curves

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

On the Existence of Hyperelliptic Curves over $Q (T)$ with Certain Jacobian Ranks