What question did this study set out to answer?

The research aims to develop and express double zeta-values related to specific root systems.

April 3, 2026Open Access

Multiple Zeta Values Related with the Zeta-function of the Root System Type A2, B2, and G2

Key Points

The research aims to develop and express double zeta-values related to specific root systems.
Introduced the double zeta-function for types A2, B2, and G2.
Utilized partial fraction decomposition to analyze values.
Explored properties of the Clausen function and Bernoulli polynomials.
Established connections between double zeta-values and Clausen function.
Presented new formulations for double zeta-values in the context of root systems.
Demonstrated the significance of Bernoulli polynomials in these calculations.

Abstract

Komori, Matsumoto and Tsumura introduced the zeta-function of the root system of type X r , where X = A, B, C, D, E, F, G.It is a multi-variable version of the Witten zeta-function with a complex simple Lie algebra.In this paper, we introduce the double zeta-function generalizing the zeta-function of the root system of type A 2 , B 2 and G 2 , and study the double zeta-values.We aim to express the double zeta-values in terms of the Clausen function et al.We remark that our idea is based on the partial fraction decomposition and the basic properties of the Clausen function and Bernoulli polynomials.

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