$p$-adic multiple $L$-functions and cyclotomic multiple harmonic values

TL;DR

This paper demonstrates that special values of $p$-adic multiple $L$-functions can be expressed using cyclotomic multiple harmonic values, linking two important concepts in number theory.

Contribution

It establishes a new explicit relationship between $p$-adic multiple $L$-function values and cyclotomic multiple harmonic values.

Findings

Expressed $p$-adic multiple $L$-function values in terms of harmonic values

Connected two significant number theoretic objects

Provided a new perspective on $p$-adic $L$-functions

Abstract

We show that the special values at tuples of positive integers of the $p$-adic multiple $L$-function introduced by the first-named author et al. can be expressed in terms of the cyclotomic multiple harmonic values introduced by the second-named author.