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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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1435-5337
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Volume 25, Issue 5

Issues

Cropping Euler factors of modular L-functions

Josep González
  • Departament de Matemàtica Aplicada IV, Universitat Politècnica de Catalunya (UPC), Av. Víctor Balaguer, s/n, E-08800 Vilanova i la Geltrú, Spain
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/ Jorge Jiménez-Urroz
  • Departament de Matemàtica Aplicada IV, Universitat Politècnica de Catalunya (UPC), Edifici C3 – Campus Nord, Jordi Girona, 1–3, E-08034 Barcelona, Spain
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/ Joan-Carles Lario
  • Departament de Matemàtica Aplicada II, Universitat Politècnica de Catalunya (UPC), Edifici Omega – Campus Nord, Jordi Girona, 1–3, E-08034 Barcelona, Spain
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Published Online: 2011-06-27 | DOI: https://doi.org/10.1515/form.2011.140

Abstract.

According to the Birch and Swinnerton-Dyer conjectures, if is an abelian variety, then its L-function must capture a substantial part of the properties of A. The smallest number field where A has all its endomorphisms defined must also play a role. This article deals with the relationship between these two objects in the specific case of modular abelian varieties associated to weight 2 newforms for the group Γ1(N). Specifically, our goal is to relate , with the order at of Euler products restricted to primes that split completely in . This is attained when a power of Af is isogenous over to the Weil restriction of the building block of Af. We give separated formulae for the CM and non-CM cases.

Keywords: L-functions; abelian varieties; distribution of Frobenius elements

About the article

Received: 2010-10-27

Revised: 2011-06-07

Published Online: 2011-06-27

Published in Print: 2013-09-01


Citation Information: Forum Mathematicum, Volume 25, Issue 5, Pages 1039–1066, ISSN (Online) 1435-5337, ISSN (Print) 0933-7741, DOI: https://doi.org/10.1515/form.2011.140.

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© 2013 by Walter de Gruyter Berlin Boston.Get Permission

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