# Sur les fonctions L de formes modulaires

Abstract : We give four contributions to the study of $L$-functions of modular forms. First, we prove that the Jacobian of a modular curve has a simple quotient of great dimension and rank $0$ and a simple quotient of great dimension and great rank. In a second contribution we prove the $1$-level density conjecture for new families of modular $L$-functions. Then, we study the distribution of the value at $1$ of the $L$-function of the symetric square of a modular form. Finally, we give, in collaboration with F. Martin, a criteria for the determination of modular forms by the special values of their $L$-functions.
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Document type :
Theses
Mathematics [math]. Université Paris Sud - Paris XI, 2001. French
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https://tel.archives-ouvertes.fr/tel-00001437
Contributor : Emmanuel Royer <>
Submitted on : Thursday, June 20, 2002 - 3:44:10 PM
Last modification on : Thursday, June 20, 2002 - 3:44:10 PM

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• HAL Id : tel-00001437, version 1

### Citation

Emmanuel Royer. Sur les fonctions L de formes modulaires. Mathematics [math]. Université Paris Sud - Paris XI, 2001. French. <tel-00001437>

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