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

Guillaume Ricotta (1) , Emmanuel Royer (2)

1 IMB - Institut de Mathématiques de Bordeaux
2 LMBP - Laboratoire de Mathématiques Blaise Pascal

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.

Domaines: Théorie des nombres [math.NT]

Guillaume Ricotta, Emmanuel Royer. Statistics for low-lying zeros of symmetric power L-functions in the level aspect. Forum Mathematicum, 2011, 23 (5), pp.969-1028. ⟨hal-00138457⟩