Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)


SIGMA 9 (2013), 061, 15 pages      arXiv:1306.6164      http://dx.doi.org/10.3842/SIGMA.2013.061
Contribution to the Special Issue in honor of Anatol Kirillov and Tetsuji Miwa

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

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

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.

Key words: multiple harmonic series; q-analogue.

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