DUALITY FORMULAS OF THE 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...
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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...
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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...
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Using the combinatorial description of shuffle product, we prove or reformulate several shuffle product formulas of multiple zeta values, including a general formula of the shuffle product of two multiple zeta values, some restricted shuffle product formulas of the product of two multiple zeta values, and a restricted shuffle product formula of the product of n multiple zeta values.
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ژورنال
عنوان ژورنال: Bulletin of the London Mathematical Society
سال: 2005
ISSN: 0024-6093,1469-2120
DOI: 10.1112/s0024609304003996