2010-10-15

Stephen Gelbart, Weizmann Institute of Science

A p-adic Integral for the Reciprocal of L-functions

Our general goal is two-fold: first, to construct $p$-adic Eisenstein measures on classical groups using the method of modular distributions and second, to apply the Langlands-Shahidi method to construct certain $p$-adic $L$-functions using Fourier expansions of these series. In the present talk, we confine ourselves with the group $SL(2)$, and we try to explain our techniques in this case. These results are joint work with S. Miller, A. Panchishkin, and F. Shahidi.