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Multiple zeta-star values and multiple integrals

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arxiv 1405.6499 v1 pith:FRIAAWHQ submitted 2014-05-26 math.NT

classification math.NT
keywords multiplevaluesintegralszetazeta-starclasssomeassociated
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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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  1. Evaluations of multiple polylogarithm functions, multiple zeta values and related zeta values

    math.NT 2019-08 conditional novelty 7.0 of 10

    The author proves several 1997 Borwein-Bradley-Broadhurst conjectures and general reduction formulas for alternating multiple zeta values using iterated integrals.

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