Relations for multiple zeta values and Mellin transforms of multiple polylogarithms

Jun Ichi Okuda, Kimio Ueno

    Research output: Contribution to journalArticle

    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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    Multiple zeta Values
    Polylogarithms
    Mellin Transform
    Generating Function

    ASJC Scopus subject areas

    • Mathematics(all)

    Cite this

    Relations for multiple zeta values and Mellin transforms of multiple polylogarithms. / Okuda, Jun Ichi; Ueno, Kimio.

    In: Publications of the Research Institute for Mathematical Sciences, Vol. 40, No. 2, 07.2004, p. 537-564.

    Research output: Contribution to journalArticle

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