4 papers
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…
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 with non-constant -invariants. Utilizing methods developed by Mic…
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…
On the Existence of Hyperelliptic Curves over with Certain Jacobian Ranks
Lucas Chen, Joshua Im, Steven J. Miller +1
Let be a hyperelliptic curve of genus , defined over . We prove the existence of infinitely many imaginary hyperelliptic curves with a fixed…