Number Theory Seminar
Ellen Eischen
Northwestern
p-adic differential operators on automorphic forms and applications
Abstract: At certain special points, the values of the Riemann zeta function and many other L-functions are algebraic, up to a well-determined transcendental factor. G. Shimura, H. Maass, and M. Harris extensively studied a class of differential operators on automorphic forms; these differential operators play an important role in proofs of algebraicity properties of many $L$-functions.
Building on work of N. Katz, we introduce a p-adic analogue of these differential operators, which should be similarly significant in the study of many p-adic L-functions, in particular p-adic L-functions attached to families of p-adic automorphic forms on unitary groups.
Wednesday September 16, 2009 at 4:00 PM in SEO 712