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Title:	Cropping Euler factors of modular L-functions
Author:	González Rovira, Josep; Jiménez Urroz, Jorge; Lario Loyo, Joan Carles
Other authors:	Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada IV; Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada II; Universitat Politècnica de Catalunya. TN - Grup de Recerca en Teoria de Nombres; Universitat Politècnica de Catalunya. MAK - Matemàtica Aplicada a la Criptografia
Abstract:	According to the Birch and Swinnerton-Dyer conjectures, if A/Q is an abelian variety, then its L-function must capture a substantial part of the properties of A. The smallest number field L 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 Af =Q associated to weight 2 newforms for the group t1(N). Specifically, our goal is to relate ords=1 L(Af =Q, s), with the order at s D 1 of Euler products restricted to primes that split completely in L. This is attained when a power of Af is isogenous over Q to the Weil restriction of the building block of Af . We give separated formulae for the CM and non-CM cases.
Subject(s):	-Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra -Abelian varieties -Frobenius algebras -Abelian varieties -Distribution of Frobenius elements -L-functions -Varietats abelianes -Matemàtica aplicada -Frobenius, Àlgebra de
Rights:	Attribution-NonCommercial-NoDerivs 3.0 Spain http://creativecommons.org/licenses/by-nc-nd/3.0/es/
Document type:	Article - Published version Article
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