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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. 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
