The p-adic L-functions of Evil Eisenstein Series

TL;DR

This paper computes the p-adic L-functions of evil Eisenstein series, demonstrating their factorization into known p-adic L-functions and a logarithmic term, confirming a conjecture by Glenn Stevens.

Contribution

It provides an explicit computation and factorization of p-adic L-functions for evil Eisenstein series, confirming a conjecture and advancing understanding of their structure.

Findings

p-adic L-functions factor as products of Kubota--Leopoldt L-functions and a logarithmic term

Confirmed Glenn Stevens' conjecture on the structure of these L-functions

Explicit formulas for the p-adic L-functions of evil Eisenstein series

Abstract

We compute the $p$-adic $L$-functions of evil Eisenstein series, showing that they factor as products of two Kubota--Leopoldt $p$-adic $L$-functions times a logarithmic term. This proves in particular a conjecture of Glenn Stevens.