Analytic constructions of p-adic L-functions and Eisenstein series

2012/04/17 by Alexei Pantchichkine, Pantchichkine, Alexei
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Analytic Number Theory Research

paper · pdf · doi:10.48550/arxiv.1204.3878

Abstract

The Fourier coefficients of the Siegel-Eisenstein series are p-adically continued for all primes p, as meromorphic functions, using the reciprocal of a product of L-functions. A construction of p-adic meromorphic families of such series is given in relation to the geometry of homogeneous spaces. Applications are given to p-adic L-functions, to Siegel's Mass Formula, to p-adic analytic families of automorphic representations. Based on author's talk for the Conference Automorphic Forms and Related Geometry, Assessing the Legacy of I.I. Piatetski-Shapiro

Citations

• On the Saito-Kurokawa lifting

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