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

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

2007-03-26

arxiv.org/abs/math/0703760v1

Mathematics

Number Theory

45 pages

Scientific paper

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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