$p$-adic Polylogarithms and $p$-adic Hecke $L$-functions for Totally Real Fields

Kenichi Bannai, Kei Hagihara, Kazuki Yamada, Shuji Yamamoto

Published 2020-03-18Version 1

The purpose of this article is to newly define the $p$-adic polylogarithm as an equivariant class in the cohomology of a certain infinite disjoint union of algebraic tori associated to a totally real field. We will then express the special values of $p$-adic $L$-functions interpolating nonpositive values of Hecke $L$-functions of the totally real field in terms of special values of these $p$-adic polylogarithms.