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JOURNALS // Symmetry, Integrability and Geometry: Methods and Applications // Archive

SIGMA, 2013 Volume 9, 061, 15 pp. (Mi sigma844)

This article is cited in 13 papers

The Algebra of a $q$-Analogue of Multiple Harmonic Series

Yoshihiro Takeyama

Division of Mathematics, Faculty of Pure and Applied Sciences, University of Tsukuba, Tsukuba, Ibaraki 305-8571, Japan

Abstract: We introduce an algebra which describes the multiplication structure of a family of $q$-series containing a $q$-analogue of multiple zeta values. The double shuffle relations are formulated in our framework. They contain a $q$-analogue of Hoffman's identity for multiple zeta values. We also discuss the dimension of the space spanned by the linear relations realized in our algebra.

Keywords: multiple harmonic series; $q$-analogue.

MSC: 11M32; 33E20

Received: June 27, 2013; in final form October 16, 2013; Published online October 22, 2013

Language: English

DOI: 10.3842/SIGMA.2013.061



Bibliographic databases:
ArXiv: 1306.6164


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