Explicit formulas of the relation between multiple zeta functions of Arakawa-Kaneko and Euler-Zagier types

2025/07/20 by Kawasaki, Naho
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2507.15034

Abstract

Multiple zeta functions of Arakawa-Kaneko and Euler-Zagier types are known as generalizations of the Riemann zeta function. In 2018, Kaneko and Tsumura proved that the multiple zeta functions of Arakawa-Kaneko type can be expressed as a \mathbb Q-linear combination of products of the ones of Euler-Zagier type and multiple zeta values. In this paper, we give explicit formulas to the above mentioned relation. Moreover, as a key of its proof, we also give certain functional equations among multi-polylogarithm functions explicitly.

Citations

• Zeta functions connecting multiple zeta values and poly-Bernoulli numbers
• A new integral-series identity of multiple zeta values and regularizations
• Multi-poly-Bernoulli numbers and related zeta functions
• Multiple zeta-star values and multiple integrals

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