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

Stephen Gelbart, Ralph Greenberg, Stephen D. Miller, Freydoon Shahidi

Research output: Chapter in Book/Report/Conference proceedingChapter

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.

Original languageEnglish (US)
Title of host publicationProgress in Mathematics
PublisherSpringer Basel
Pages193-208
Number of pages16
DOIs
StatePublished - 2017

Publication series

NameProgress in Mathematics
Volume323
ISSN (Print)0743-1643
ISSN (Electronic)2296-505X

All Science Journal Classification (ASJC) codes

  • Analysis
  • Algebra and Number Theory
  • Geometry and Topology

Keywords

  • Irregular primes
  • Iwasawa algebra
  • Riemann zeta-function
  • p-Adic L-Functions

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