Statistics for low-lying zeros of symmetric power L-functions in the level aspect

Ricotta, Guillaume; Royer, Emmanuel

Statistics for low-lying zeros of symmetric power L-functions in the level aspect

Authors

Description

We study one-level and two-level densities for low lying zeros of symmetric power L-functions in the level aspect. It allows us to completely determine the symmetry types of some families of symmetric power L-functions with prescribed sign of functional equation. We also compute the moments of one-level density and exhibit mock-Gaussian behavior discovered by Hughes & Rudnick.
45 pages