Seminar in Algebraic Geometry and Number Theory

Abstract: Iwaniec, Luo and Sarnak has (partially) confirmed the Katz-Sarnak heuristic (for the one-level density) in several families of classical automorphic L-functions. In this talk, I will discuss how we can use zero-density estimates for Dirichlet L-functions to extend the unconditional part of Iwaniec-Luo-Sarnak’s work in the family of L-functions attached to holomorphic newforms of fixed even weight and prime level tending to infinity. This is joint work with Lucile Devin and Daniel Fiorilli.