Multitangent functions and symmetric multiple zeta values

Abstract

In this paper, we give a formula that connects two variants of multiple zeta values; multitangent functions and symmetric multiple zeta values. As an application of this formula, we give two results. First, we prove Bouillot's conjecture on the structures of the algebra of multitangent functions. Second, we prove an analogue of the linear part of Kawashima's relation for symmetric multiple zeta values.

Theorems & Definitions (19)

• Theorem 1: Bou14AlgMTGF
• Example 2
• Example 3
• Conjecture 4: Bouillot, Bou14AlgMTGF
• Theorem 5: Bouillot, Bou14AlgMTGF
• Theorem 6: Yasuda, Yas
• Theorem 7
• Theorem 8
• Theorem 9: Analogue of Kawashima relation for symmetric multiple zeta values
• proof : Proof of Theorem \ref{['thm:main']}