Special values of multiple polylogarithms
نویسندگان
چکیده
منابع مشابه
Special Values of Multiple Polylogarithms
Historically the polylogarithm has attracted specialists and non specialists alike with its lovely evaluations Much the same can be said for Euler sums or multiple harmonic sums which within the past decade have arisen in combinatorics knot theory and high energy physics More recently we have been forced to consider multidimensional extensions encompassing the classical polylogarithm Euler sums...
متن کاملSpecial Values of Multidimensional Polylogarithms
Historically, the polylogarithm has attracted specialists and non-specialists alike with its lovely evaluations. Much the same can be said for Euler sums (or multiple harmonic sums), which, within the past decade, have arisen in combinatorics, knot 1 theory and high-energy physics. More recently, we have been forced to consider mul-tidimensional extensions encompassing the classical polylogarit...
متن کاملDouble 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 ...
متن کاملLinear Relations of Special Values of Multiple Polylogarithms at Roots of Unity
In this paper for any positive integer N we shall study the special values of multiple polylogarithms at Nth roots of unity, called multiple polylogarithmic values (MPVs) of level N . These objects are generalizations of multiple zeta values and alternating Euler sums. Our primary goal is to investigate the relations among the MPVs of the same weight and level by using the distribution relation...
متن کاملMultiple Polylogarithms: An Introduction
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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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 2000
ISSN: 0002-9947,1088-6850
DOI: 10.1090/s0002-9947-00-02616-7