Congruence identities of regularized multiple zeta values involving a pair of index sets
نویسندگان
چکیده
منابع مشابه
Algorithms for Some Euler-Type Identities for Multiple Zeta Values
. . . , s k are positive integers with s 1 > 1. For k ≤ n, let E(2n, k) be the sum of all multiple zeta values with even arguments whose weight is 2n and whose depth is k. The well-known result E(2n, 2) = 3ζ(2n)/4was extended to E(2n, 3) and E(2n, 4) by Z. Shen and T. Cai. Applying the theory of symmetric functions, Hoffman gave an explicit generating function for the numbers E(2n, k) and then ...
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Multiple zeta values (MZVs, also called Euler sums or multiple harmonic series) are nested generalizations of the classical Riemann zeta function evaluated at integer values. The fact that an integral representation of MZVs obeys a shuue product rule allows the possibility of a combi-natorial approach to them. Using this approach we prove a longstanding conjecture of Don Zagier about MZVs with ...
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Multiple zeta values (MZVs) in the usual sense are the special values of multiple variable zeta functions at positive integers. Their extensive studies are important in both mathematics and physics with broad connections and applications. In contrast, very little is known about the special values of multiple zeta functions at non-positive integers since the values are usually singular. We defin...
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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: International Journal of Number Theory
سال: 2016
ISSN: 1793-0421,1793-7310
DOI: 10.1142/s179304211650024x