Number Theory Seminar

Title: Symmetric powers of Hilbert modular forms and p-adic L-functions.

Abstract: To a Hilbert modular form one may attach a p-adic analytic L-function interpolating certain special values of the usual L-function. Conjectures in the style of Mazur, Tate and Teitelbaum prescribe the order of vanishing and first Taylor coefficient of such p-adic L-functions, the first coefficient being controlled by an L-invariant which has conjectural (arithmetic) value defined by Greenberg and Benois. I will explain how to compute arithmetic L-invariants for symmetric powers of Iwahori level Hilbert modular forms using Langlands functoriality and triangulations of (phi, Gamma)-modules on eigenvarieties. This is based on joint work with Robert Harron.