Fundamentals of p-adic multiple L-functions and evaluation of their special values

Abstract

We construct $p$-adic multiple $L$-functions in several variables, which are generalizations of the classical Kubota-Leopoldt $p$-adic $L$-functions, by using a specific $p$-adic measure. Our construction is from the $p$-adic analytic side of view, and we establish various fundamental properties of these functions.

This paper is the p-adic part of our original article arXiv:math/1309.3982 which was divided into the complex part and the p-adic part