3 papers
math.NT2025
Counting newforms with prescribed ramified supercuspidal components
Andrew Knightly, Kimball Martin
We give a formula for the number of newforms in that have prescribed ramified supercuspidal components at a set of primes dividing . This dimen…
math.NT2023
Counting locally supercuspidal newforms
Andrew Knightly
The trace formula is a versatile tool for computing sums of spectral data across families of automorphic forms. Using specialized test functions, one can treat small families with…
math.NT2018
Weighted distribution of low-lying zeros of GL(2) L-functions
Andrew Knightly, Caroline Reno
We show that if the zeros of an automorphic -function are weighted by the central value of the -function or a quadratic imaginary base change, then for certain families of ho…