EVENT DETAILS AND ABSTRACT

Title: Critical p-adic L-functions
Speaker: Joel Bellaiche
Speaker Info: Brandeis
Brief Description:
Special Note:
Abstract:

For three decades, it was only possible to attach a p-adic L-function to a cuspidal eigenform of weight k whose slope (that is, p-valuation of the eigenvalue for the operator U_p) was strictly less than k+1. More recently, Stevens and Pollack explained how to attach, in a natural way, a p-adic L-function for some slope k+1 (or critical slope) cuspidal eigenforms, namely the cuspidal forms that are not critical. I shall explain how, using our knowledge of the geometry of the eigencurve, one can extend their work and define natural p-adic L-functions for the missing cuspidal eigenforms as well as for the evil Eisenstein series. I shall also show that all those p-adic L-functions, old and new, fit in a two-variables p-adic L-function on the eigencurve, extending earlier results of Stevens, Panchishkin and Emerton.