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Statistics for low-lying zeros of symmetric power L-functions in the level aspect
-
Guillaume Ricotta
and
Emmanuel Royer
Published/Copyright:
May 31, 2010
Abstract
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.
Keywords.: L-functions; automorphic forms; symmetric powers; random matrix theory; statistics; zeroes
Received: 2007-05-10
Revised: 2009-11-30
Published Online: 2010-05-31
Published in Print: 2011-September
© de Gruyter 2011
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Keywords for this article
L-functions;
automorphic forms;
symmetric powers;
random matrix theory;
statistics;
zeroes
Articles in the same Issue
- Quantum unique ergodicity of Eisenstein series on the Hilbert modular group over a totally real field
- On the self-intersection cycle of surfaces and some classical formulas for their secant varieties
- Wolff potentials and the 3-d wave operator
- Statistics for low-lying zeros of symmetric power L-functions in the level aspect
- Simple Harish-Chandra modules, intermediate series modules, and Verma modules over the loop-Virasoro algebra
- On the classification of fake lens spaces
- Cohomology and removable subsets
