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- W2950526412 abstract "It's well known that multiple polylogarithms give rise to good unipotent variations of mixed Hodge-Tate structures. In this paper we shall {em explicitly} determine these structures related to multiple logarithms and some other multiple polylogarithms of lower weights. The purpose of this explicit construction is to give some important applications: First we study of the limit mixed Hodge-Tate structures and make a conjecture relating the variations of mixed Hodge-Tate structures of multiple logarithms to those of general multiple {em poly}logarithms. Then following Deligne and Beilinson we describe an approach to defining the single-valued real analytic version of the multiple polylogarithms which generalizes the well-known result of Zagier on classical polylogarithms. In the process we find some interesting identities relating single-valued multiple polylogarithms of the same weight $k$ when $k=2$ and 3. At the end of this paper, motivated by Zagier's conjecture we pose a problem which relates the special values of multiple Dedekind zeta functions of a number field to the single-valued version of multiple polylogarithms." @default.
- W2950526412 created "2019-06-27" @default.
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- W2950526412 date "2003-02-05" @default.
- W2950526412 modified "2023-09-23" @default.
- W2950526412 title "Variations of mixed Hodge structures of multiple polylogarithms" @default.
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- W2950526412 doi "https://doi.org/10.48550/arxiv.math/0302055" @default.
- W2950526412 hasPublicationYear "2003" @default.
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