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Cropping Euler factors of modular L-functions
González Rovira, Josep; Jiménez Urroz, Jorge; Lario Loyo, Joan Carles
Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada IV; Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada II; Universitat Politècnica de Catalunya. TN - Teoria de Nombres; Universitat Politècnica de Catalunya. MAK - Matemàtica Aplicada a la Criptografia
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.
Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra
Abelian varieties
Frobenius algebras
Abelian varieties
Distribution of Frobenius elements
Varietats abelianes
Matemàtica aplicada
Frobenius, Àlgebra de
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