Article

# Derivation and double shuffle relations for multiple zeta values

Collège de France, Lutetia Parisorum, Île-de-France, France
(Impact Factor: 0.99). 03/2006; 142(02). DOI: 10.1112/S0010437X0500182X
Source: OAI

ABSTRACT Derivation and extended double shuffle (EDS) relations for multiple zeta values (MZVs) are proved. Related algebraic structures of MZVs, as well as a version of EDS relations are also studied.

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• "Several of the papers mentioned above also contain formulas of a similar flavor for the values of more general " multiple zeta values " defined in terms of several integer-valued parameters; see also [14], [20], [29], [45] for related results. The results described above may not make evident why it is natural to consider ω(s) as a true Dirichlet series (that is, as a function of a complex variable s), but plenty of precedents from the history of analytic number theory suggest that this is worth doing. "
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• "), where ζ X stands for the 'shuffle regularized' value, which is the constant term of the shuffle regularized polynomial defined in [19]. "
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• "is equivalent to Z x n in the present paper. The proof of (2.13) in [10] is summarized in the proof of [15, Lemma 3.1] (see [15, (3.11)]). "
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