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.
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