Relations for multiple zeta values and Mellin transforms of multiple polylogarithms

Jun Ichi Okuda, Kimio Ueno

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    17 Citations (Scopus)

    Abstract

    In this paper a relationship between the Ohno relation for multiple zeta values and multiple polylogarithms are discussed. First we introduce generating functions for the Ohno relation, and investigate their properties. We show that there exists a subfamily of the Ohno relation which recovers algebraically its totality. This is proved through analysis of Mellin transform of multiple polylogarithms. Furthermore, this subfamily is shown to be converted to the Landen connection formula for multiple polylogarithms by inverse Mellin transform.

    Original languageEnglish
    Pages (from-to)537-564
    Number of pages28
    JournalPublications of the Research Institute for Mathematical Sciences
    Volume40
    Issue number2
    Publication statusPublished - 2004 Jul

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    ASJC Scopus subject areas

    • Mathematics(all)

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