Extending the unconditional support in an Iwaniec--Luo--Sarnak family
Heilbronn Number Theory Seminar
2nd November 2022, 4:00 pm – 5:00 pm
Fry Building, 2.04
We study the harmonically weighted one-level density of low-lying zeros of L-functions attached to holomorphic cusps forms of fixed even weight $k$ and prime level tending to infinity. This family was proved to be of orthogonal type by Iwaniec, Luo and Sarnak who obtained the predicted main term for test functions having Fourier transform supported in $(-\tfrac32,\tfrac32)$ unconditionally. Using zero-density estimates for Dirichlet L-function, we extend this admissible support to $(-\Theta_k;\Theta_k)$, where $\Theta_2 = 1.866\dots$ and $\Theta_k \rightarrow 2$ as $k$ grows.
This is joint work with Daniel Fiorilli and Anders Södergren.