Estimates on Eisenstein Distributions for Reciprocals of p-Adic L-Functions: The Case of Irregular Primes

Abstract

We consider the p-adic distributions derived from Eisenstein series studied by Gelbart, Miller, Panchishkin, and Shahidi, whose Mellin transforms are reciprocals of the Kubota-Leopoldt p-adic L-function. These distributions were shown there to be measures when p is regular. They fail to be measures when p is irregular; in this paper, we give quantitative estimates that describe their behavior more precisely.