Shuffle product of finite multiple polylogarithms
نویسندگان
چکیده
منابع مشابه
Double Shuffle Relations of Special Values of Multiple Polylogarithms
In this paper we shall study the special values of multiple polylogarithms atmth roots of unity, called multiple polylogarithmic values (MPVs) of depth m. These objects are generalizations of multiple zeta values and alternating Euler sums. Our primary goal is to investigate the relations between the special values by using (extended) double shuffle relations. In particular we want to know for ...
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when s1, . . . , sk are positive integers and z a complex number in the unit disk. For k = 1, this is the classical polylogarithm Lis (z). These multiple polylogarithms can be defined also in terms of iterated Chen integrals and satisfy shuffle relations. Multiple polylogarithms in several variables are defined for si ≥ 1 and |zi | < 1(1 ≤ i ≤ k) by Li(s1,...,sk)(z1, . . . , zk) = ∑ n1>n2>···>n...
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Contents 1. Introduction 1 1.1. History and motivation 1 1.2. What we do 3 1.3. Plan of the article 3 1.4. Conventions and notations 4 2. The De Rham fundamental groupoid of a punctured elliptic curve 5 2.1. Nilpotent vector bundles 5 2.2. Nilpotent connections with simple poles at the origin 6 3. A universal flat connection over the upper-half plane 10 3.1. Combinatorial conventions and lemmas...
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ژورنال
عنوان ژورنال: manuscripta mathematica
سال: 2016
ISSN: 0025-2611,1432-1785
DOI: 10.1007/s00229-016-0856-9