Algebraic setup of non-strict multiple zeta values

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7 Algebraic setup of non - strict multiple zeta values Shuichi Muneta

where k1, k2, . . . , kn are positive integers and k1 ≥ 2. Considerable amount of work on MZVs has been done from various aspects and interests. The MZVs have many relations among them (duality formula, sum formula, Hoffman’s relations, Ohno’s relations, derivation relations and cyclic sum relations, cf. [H1], [HO], [IKZ], [O]) and these relations can be described in purely algebraic manner (cf...

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Algebraic Aspects of Multiple Zeta Values

Multiple zeta values have been studied by a wide variety of methods. In this article we summarize some of the results about them that can be obtained by an algebraic approach. This involves “coding” the multiple zeta values by monomials in two noncommuting variables x and y. Multiple zeta values can then be thought of as defining a map ζ : H0 → R from a graded rational vector space H0 generated...

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ON THE SUM FORMULA FOR THE q-ANALOGUE OF NON-STRICT MULTIPLE ZETA VALUES

In this article, the q-analogues of the linear relations of non-strict multiple zeta values called “the sum formula” and “the cyclic sum formula” are established.

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A q-ANALOGUE OF NON-STRICT MULTIPLE ZETA VALUES AND BASIC HYPERGEOMETRIC SERIES

We consider the generating function for a q-analogue of non-strict multiple zeta values (or multiple zeta-star values) and prove an explicit formula for it in terms of a basic hypergeometric series 3φ2. By specializing the variables in the generating function, we reproduce the sum formula obtained by Ohno and Okuda and get some relations in the case of full height.

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Aspectsof Multiple Zeta Values

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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ژورنال

عنوان ژورنال: Acta Arithmetica

سال: 2009

ISSN: 0065-1036,1730-6264

DOI: 10.4064/aa136-1-2