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Forum Mathematicum

Managing Editor: Bruinier, Jan Hendrik

Ed. by Blomer, Valentin / Cohen, Frederick R. / Droste, Manfred / Duzaar, Frank / Echterhoff, Siegfried / Frahm, Jan / Gordina, Maria / Shahidi, Freydoon / Sogge, Christopher D. / Takayama, Shigeharu / Wienhard, Anna

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CiteScore 2018: 0.71

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Source Normalized Impact per Paper (SNIP) 2018: 0.964

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Volume 23, Issue 5


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

Guillaume Ricotta / Emmanuel Royer
  • Laboratoire de mathématiques, Clermont Université, Université Blaise Pascal, BP 10448, 63000 Clermont-Ferrand, France.
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Published Online: 2010-05-31 | DOI: https://doi.org/10.1515/form.2011.035


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

About the article

Received: 2007-05-10

Revised: 2009-11-30

Published Online: 2010-05-31

Published in Print: 2011-09-01

Citation Information: Forum Mathematicum, Volume 23, Issue 5, Pages 969–1028, ISSN (Online) 1435-5337, ISSN (Print) 0933-7741, DOI: https://doi.org/10.1515/form.2011.035.

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