Breadcrumb
Modular Forms and Congruences
Wed 20 February 2013, 16:00
Nicolas Billerey
Clermont-Ferrand
Organisers: Tim Dokchitser, Daniel Loughran
ABSTRACT
In the sixties, Serre gave an interpretation of the congruences satisfied by the Ramanujan Tau function in terms of Galois representations. The precise determination by Serre and Swinnerton-Dyer of the image of these representations allowed them to give a complete list of the so-called exceptional primes for the Delta function. Their result was later (1985) generalized by Ribet in a non-effective way. After briefly recalling the history of the problem, I will explain how to obtain an explicit version of Ribet's theorem. This is a joint work with Luis Dieulefait.