An introduction to Eisenstein measures

Abstract

This paper provides an introduction to Eisenstein measures, a powerful tool for constructing certain $p$-adic $L$-functions. First seen in Serre's realization of $p$-adic Dedekind zeta functions associated to totally real fields, Eisenstein measures provide a way to extend the style of congruences Kummer observed for values of the Riemann zeta function (so-called {\em Kummer congruences}) to certain other $L$-functions. In addition to tracing key developments, we discuss some challenges that arise in more general settings, concluding with some that remain open.

Accepted for publication in Journal de Théorie des Nombres de Bordeaux

References in corpus (4)

• Algebraic topology and modular forms
• Higher Hida and Coleman theories on the modular curve
• Modular sheaves of de Rham classes on Hilbert formal modular schemes for unramified primes
• Families of Differential Operators for Overconvergent Hilbert Modular Forms

Cited by in corpus (1)

• Automorphic Forms on Unitary Groups