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

TL;DR

This paper develops a method for p-adic continuation of Fourier coefficients of Siegel-Eisenstein series, linking them to L-functions and geometric structures, with applications to p-adic L-functions, automorphic forms, and mass formulas.

Contribution

It introduces a new construction of p-adic meromorphic families of Eisenstein series using geometric and L-function techniques, extending previous work in the area.

Findings

Fourier coefficients are p-adically continued as meromorphic functions.

Constructs p-adic families of Eisenstein series related to homogeneous space geometry.

Applications include new insights into p-adic L-functions and automorphic representation families.

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