The p-Adic Eisenstein Measure and Shahidi-type p-Adic Integral for SL(2)

Stephen Gelbart (1) , Stephen D. Miller (2) , Alexei Panchishkin (3) , Freydoon Shahidi (4)

1 Department of Mathematics
2 Department of Mathematics
3 IF - Institut Fourier
4 Department of Mathematics

Our general goal is two-fold: first, to construct p-adic Eisenstein measures on classical groups using the method of modular distibutions and second, to apply Shahidi-type theory to construct certain p-adic L-functions using Fourier expansions of these series. In the present paper we confine ourselves with the group SL(2), and we try to explain our techniques in this case.

Mots clés: Modular forms; p-adic L-functions; Eisenstein series

Domaines: Théorie des nombres [math.NT]

Stephen Gelbart, Stephen D. Miller, Alexei Panchishkin, Freydoon Shahidi. The p-Adic Eisenstein Measure and Shahidi-type p-Adic Integral for SL(2). 2009. ⟨hal-00446071v3⟩