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

2007/03/26 by Ricotta, Guillaume, Royer, Emmanuel
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.math/0703760

Abstract

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.

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