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

We study one-level and two-level densities for low-lying zeros of symmetric power $L$-functions in the level aspect. This 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.

Article de revue

Forum Mathematicum 23, No. 5, 969-1028