On the Functional Relations for the Euler-Zagier Multiple Zeta-functions

Abstract

The purpose of this paper is to formulate problem about existence or non-existence of functional relations for the Euler-Zagier multiple zeta-functions and solve this problem. This problem is a functional analogue of the problem about existence or non-existence of relations among the multiple zeta values. By our results, we can solve a functional analogue of the problem about the dimension of the $\mathbb{Q}$-vector space spanned by the multiple zeta values.