A p-adic integral for the reciprocal of L-functions

2010/01/12 by Stephen Gelbart, Stephen D. Miller, Gelbart, Stephen +5
Mathematics · #FOS: Mathematics #Number Theory (math.NT) #math.NT

paper · pdf · doi:10.48550/arxiv.1001.1913

16 pages, to appear in a Contemp. Math. (AMS) volume in memory of Ilya Piatetski-Shapiro

arxiv created 2012/12/19 · arxiv updated 2012/12/20

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.

Related

• p-adic Measures for Reciprocals of L-functions of Totally Real Fields
• Estimates on Eisenstein distributions for reciprocals of p-adic L-functions: the case of irregular primes
• A Summary of the Langlands-Shahidi Method of Constructing L-functions
• Analytic constructions of p-adic L-functions and Eisenstein series
• p-adic L-functions on metaplectic groups