$p$-adic Measures for Reciprocals of $L$-functions of Totally Real Fields

TL;DR

This paper develops p-adic measures that interpolate reciprocal values of p-adic L-functions for totally real fields, using Eisenstein series analysis, advancing understanding of p-adic number theory and L-functions.

Contribution

It introduces a new construction of p-adic measures for reciprocals of p-adic L-functions of totally real fields via Eisenstein series analysis.

Findings

Constructed p-adic measures for reciprocals of p-adic L-functions.

Connected Eisenstein series' non-constant terms to measure construction.

Provides tools for further study of p-adic properties of L-functions.

Abstract

We construct $p$-adic measures which interpolate the special values of reciprocals of $p$-adic $L$-functions of totally real number fields $K$ at negative integers. These measures are defined by analyzing the non-constant term of partial Eisenstein series of the Hilbert modular group of $K$.