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Formules de trace en niveau primaire et non annulation de valeurs centrales de fonctions L automorphes

Abstract : The study of the analytical properties of the modular L-functions is a deep subject in number theory. Up to now, the properties have essentially been established in the case of prime or squarefree level. The aim of this thesis is to give the analytic properties in the arithmetically opposite case of prime power level. The family of L-functions under consideration is the one obtained when the valuation of the level is varying. In particular, we provide a trace formula that allows to compute the third moment of the central values of modular L-functions and to study the vanishing of these L values.
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Djamel Rouymi. Formules de trace en niveau primaire et non annulation de valeurs centrales de fonctions L automorphes. Mathématiques générales [math.GM]. Université Henri Poincaré - Nancy 1, 2009. Français. ⟨NNT : 2009NAN10081⟩. ⟨tel-01748343⟩

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