Lucas Chen

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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.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…

Product and Quotient Set Dominance in Finite Groups

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

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