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Symmetry, Integrability and Geometry: Methods and Applications, 2013, Volume 9, 061, 15 pp.
DOI: https://doi.org/10.3842/SIGMA.2013.061 (Mi sigma844) 		 
This article is cited in 12 scientific papers (total in 12 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
Full-text PDF (383 kB) Citations (12)
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DOI: https://doi.org/10.3842/SIGMA.2013.061
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.
Received: June 27, 2013; in final form October 16, 2013; Published online October 22, 2013
Bibliographic databases:
Document Type: Article
MSC: 11M32; 33E20
Language: English
Citation: Yoshihiro Takeyama, “The Algebra of a $q$-Analogue of Multiple Harmonic Series”, SIGMA, 9 (2013), 061, 15 pp.
Citation in format AMSBIB
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\by Yoshihiro~Takeyama
\paper The Algebra of a~$q$-Analogue of Multiple Harmonic Series
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\papernumber 061
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    • This publication is cited in the following 12 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Symmetry, Integrability and Geometry: Methods and Applications
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