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

Guillaume Ricotta·Emmanuel Royer
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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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Guillaume Ricotta, Emmanuel Royer. 2007-03-26. Statistics for low-lying zeros of symmetric power L-functions in the level aspect. https://arxiv.org/abs/math/0703760

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