5 F eb 2 00 3 Analytic continuation of multiple polylogarithms ∗
نویسنده
چکیده
In this paper we shall define the analytic continuation of the multiple polylogarithms by using Chen’s theory of iterated path integrals and compute the monodromy of all multiple logarithms explicitly.
منابع مشابه
ar X iv : m at h / 03 02 05 5 v 2 [ m at h . A G ] 5 F eb 2 00 3 Variations of Mixed Hodge Structures of Multiple Polylogarithms ∗
It’s well known that multiple polylogarithms give rise to good unipotent variations of mixed Hodge-Tate structures. In this paper we shall 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 struc...
متن کاملar X iv : m at h / 03 02 05 5 v 1 [ m at h . A G ] 5 F eb 2 00 3 Variations of Mixed Hodge Structures of Multiple Polylogarithms ∗
It’s well known that multiple polylogarithms give rise to good unipotent variations of mixed Hodge-Tate structures. In this paper we shall 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 struc...
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The fractional polylogarithms, depending on a complex parameter α, are defined by a series which is analytic inside the unit disk. After an elementary conversion of the series into an integral presentation, we show that the fractional polylogarithms are multivalued analytic functions in the complex plane minus 0 and 1. For non-integer values of α, we prove the analytic continuation, compute the...
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