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

TL;DR

This paper constructs multivariable p-adic multiple L-functions generalizing classical p-adic L-functions, establishing their fundamental properties from a p-adic analytic perspective.

Contribution

It introduces a new construction of p-adic multiple L-functions using p-adic measures, extending classical theories.

Findings

Construction of p-adic multiple L-functions in several variables

Establishment of fundamental properties of these functions

Generalization of classical p-adic L-functions

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.