Multiple polylogarithm values at roots of unity
نویسندگان
چکیده
منابع مشابه
Multiple polylogarithm values at roots of unity
For any positive integer N let μN be the group of the N th roots of unity. In this note we shall study the Q-linear relations among the values of multiple polylogarithms evaluated at μN . We show that the standard relations considered by Racinet do not provide all the possible relations in the following cases: (i) level N = 4, weight w = 3 or 4, and (ii) w = 2, 7 <N < 50, and N is a power of 2 ...
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Let N be a positive integer. In this paper we shall study the special values of multiple polylogarithms atNth roots of unity, called multiple polylogarithm values (MPVs) of levelN . These objects are generalizations of multiple zeta values and alternating Euler sums, which was studied by Euler, and more recently, many mathematicians and theoretical physicists.. Our primary goal in this paper is...
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We evaluate multiple polylogarithm values at sixth roots of unity up to weight six, i.e. of the form G(a1, . . . , aw; 1) where the indices ai are equal to zero or a sixth root of unity, with a1 6= 1. For w ≤ 6, we construct bases of the linear spaces generated by the real and imaginary parts of G(a1, . . . , aw; 1) and obtain a table for expressing them as linear combinations of the elements o...
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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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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 . By standard conjectures linear relations exist only between MPVs of the same weight. LetMPVZ(w,N) be the Z-module spanned by MPVs of weight w and level N . Our main interest is to investigate for what w and N the...
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ژورنال
عنوان ژورنال: Comptes Rendus Mathematique
سال: 2008
ISSN: 1631-073X
DOI: 10.1016/j.crma.2008.09.011