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arXiv · 2101.01879

An introduction to Eisenstein measures

E. E. Eischen
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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.

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E. E. Eischen. 2021-02-02. An introduction to Eisenstein measures. https://doi.org/10.5802/jtnb.1178

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