Multiple Zeta Values and Ideles

Abstract

In this paper we give two idelic representations of the multiple zeta values - one using iterated integrals over the finite ideles and the other using iterated integrals over the idele class group. Each of the representations leads to a shuffle relation. Thus, we recover in a unified way the two types of shuffle relations of multiple zeta values via the iterated integrals over finite ideles and via iterated integrals over the idele class group.

arXiv commentThis paper is a substantially revised version of the preprint "Multiple Zeta Functions, Modular Forms and Adeles" from 2006; better arranged comated to the previous version; 10 pages