A p-adic integral for the reciprocal of L-functions
Number Theory
2012-12-20 v5
Abstract
We introduce an analog of part of the Langlands-Shahidi method to the p-adic setting, constructing reciprocals of certain p-adic L-functions using the nonconstant terms of the Fourier expansions of Eisenstein series. We carry out the method for the group SL(2), and give explicit p-adic measures whose Mellin transforms are reciprocals of Dirichlet L-functions.
Keywords
Cite
@article{arxiv.1001.1913,
title = {A p-adic integral for the reciprocal of L-functions},
author = {Stephen Gelbart and Stephen D. Miller and Alexei Pantchichkine and Freydoon Shahidi},
journal= {arXiv preprint arXiv:1001.1913},
year = {2012}
}
Comments
16 pages, to appear in a Contemp. Math. (AMS) volume in memory of Ilya Piatetski-Shapiro