Bowman-Bradley type theorem for finite multiple zeta values
نویسندگان
چکیده
منابع مشابه
On a Reciprocity Law for Finite Multiple Zeta Values
Abstract. It was shown in [7, 9] that harmonic numbers satisfy certain reciprocity relations, which are in particular useful for the analysis of the quickselect algorithm. The aim of this work is to show that a reciprocity relation from [7, 9] can be generalized to finite variants of multiple zeta values, involving a finite variant of the shuffle identity for multiple zeta values. We present th...
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for any collection of positive integers s1, s2, . . . , sl. By definition, Lis(1) = ζ(s), s ∈ Z, s1 ≥ 2, s2 ≥ 1, . . . , sl ≥ 1. (4.2) Taking, as before for multiple zeta values, Lixs(z) := Lis(z), Li1(z) := 1, (4.3) let us extend action of the map Li : w 7→ Liw(z) by linearity on the graded algebra H (not H, since multi-indices are coded by words in H). Lemma 4.1. Let w ∈ H be an arbitrary non...
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It is now a good time to go back to the MZV story. where F (a, b; c; z) denotes the hypergeometric function and i = √ −1. Proof. Routine verification (with a help of Lemma 4.1 for the left-hand side) shows that the both sides of the required equality are annihilated by action of the differential operator (1 − z) d dz 2 z d dz 2 − t 4 ; in addition, the first terms in z-expansions of the both si...
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ژورنال
عنوان ژورنال: Tohoku Mathematical Journal
سال: 2016
ISSN: 0040-8735
DOI: 10.2748/tmj/1466172771