Conférence "Zeta Functions"
21 - 25 juin 2010
Organisateurs: Michel Balazard (CNRS, Laboratoire Poncelet), Michael Tsfasman (CNRS, Laboratoire Poncelet, Institut des Problèmes de Transmission de l'Information), Alexey Zykin (Laboratoire Poncelet, Haute Ecole d'Economie)
Vendredi 25 juin, 10:00 - 11:00
We construct p-adic L-functions as Mellin transforms of certain distributions attached to Euler products. The method of modular distributions makes it possible to construct in many cases such L-functions from the Fourier coefficients of modular forms. I discuss resultats, projects and recent applications related to each other by the method of modular distributions: 1) p-adic version of Shahidi's type integral ("The p-adic Eisenstein measure and Shahidi-type p-adic integral for SL(2)", in preparation, with participation of S. Gelbart, S. Miller, F. Shahidi) 2) A p-adic interpolation of the special values of Lfunctions of Rankin and of Garrett (with S.Bocherer, ...) 3) Relations with elliptic units and points of Stark-Heegner