Multiple zeta-star values and multiple integrals

2014/05/26 by Yamamoto, Shuji · 2 citations
#FOS: Mathematics #Number Theory (math.NT) #Primary 11M32 #Secondary 40B05

paper · doi:10.48550/arxiv.1405.6499

Abstract

We prove a kind of integral expressions for finite multiple harmonic sums and multiple zeta-star values. Moreover, we introduce a class of multiple integrals, associated with some combinatorial data (called 2-labeled posets). This class includes both multiple zeta and zeta-star values of Euler-Zagier type, and also several other types of multiple zeta values. We show that these integrals can be used to obtain some relations among such zeta values quite transparently.

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• A map between arborifications of multiple zeta values
• Explicit formulas of the relation between multiple zeta functions of Arakawa-Kaneko and Euler-Zagier types

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