David Hansen (Jussieu)
p-adic L-functions for GL(2)

Abstract: I'll describe a construction which associates a canonical p-adic L-function with a "non-critically refined" cohomological cuspidal automorphic representation of GL2(A_F) over an arbitrary number field F. These L-functions have good interpolation and growth properties, and they deform well over eigenvarieties. The main idea is the construction of certain canonical "p-adic period functionals" out of overconvergent cohomology. In the first half of the talk, I'll describe the main results and try to put them in context. In the second half, I'll focus on the period functionals.