Some relations deduced from regularized double shuffle relations of multiple zeta values

Abstract

It is conjectured that the regularized double shuffle relations give all algebraic relations among the multiple zeta values, and hence all other algebraic relations should be deduced from the regularized double shuffle relations. In this paper, we provide as many as the relations which can be derived from the regularized double shuffle relations, for example, the weighted sum formula of Guo and Xie, some evaluation formulas with even arguments and the restricted sum formulas of Hoffman and their generalizations.