Shuffle products for multiple zeta values and partial fraction decompositions of zeta-functions of root systems

Abstract

The shuffle product plays an important role in the study of multiple zeta values. This is expressed in terms of multiple integrals, and also as a product in a certain non-commutative polynomial algebra over the rationals in two indeterminates. In this paper, we give a new interpretation of the shuffle product. In fact, we prove that the procedure of shuffle products essentially coincides with that of partial fraction decompositions of multiple zeta values of root systems. As an application, we give a proof of extended double shuffle relations without using Drinfel'd integral expressions for multiple zeta values. Furthermore, our argument enables us to give some functional relations which include double shuffle relations.

18 pages

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Cited by in corpus (6)

• Extended double shuffle relations and the generating function of triple zeta values of any fixed weight
• A study on multiple zeta values from the viewpoint of zeta-functions of root systems
• Truncated $t$-adic symmetric multiple zeta values and double shuffle relations
• A parameterized generalization of the sum formula for quadruple zeta values
• An overview and supplements to the theory of functional relations for zeta-functions of root systems
• Functional relations for zeta-functions of weight lattices of Lie groups of type $A_3$