# Séminaires : Séminaire Théorie des Nombres

 Equipe(s) : tn, Responsables : Ziyang Gao, Marc Hindry, Bruno Kahn, João Pedro P. dos Santos Email des responsables : ziyang.gao@imj-prg.fr Salle : Adresse : Description http://www.imj-prg.fr/tn/STN/stnj.html

 Orateur(s) H. Hida - , Titre The Integral Basis Problem of Eichler Date 28/06/2004 Horaire 14:00 à 16:00 Diffusion Résume Writing down a given modular forms as a linearcombination of theta series is a classical problem.The celebrated formula of Jacobi:"the number of ways of expressing an odd positive integer$n$ as sums of four squares is equal to $8$ times the sumof positive divisors of $n$"is an identity of the theta series(of the sum of four squares) and an Eisenstein series,which is the origin of the Siegel-Weil formula.Eichler solved this problem for non-Eisenstein seriesfor the norm forms of division quaternion algebrasover the rational numbers, and his work is vastly generalizedby Jacquet-Langlands to any quaternion algebra over any number field.I would like to present a simple argument (assuming the theoremof Jacquet-Langlands) how to express a given integral Hilbert modularform into an integral linear combination of such theta series. Salle Adresse