Interpolation of q-analogue of multiple zeta and zeta-star values

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• 作者：Noriko Wakabayashi ^{noriko-w@fc.ritsumei.ac.jp}
• 关键词：t-qMZVs ; Harmonic products ; Kawashima type relation ; Cyclic sum formula ; Hoffman type relation
• 刊名：Journal of Number Theory
• 出版年：2017
• 出版时间：May 2017
• 年：2017
• 卷：174
• 期：Complete
• 页码：26-39
• 全文大小：299 K
• 卷排序：174

文摘

We know at least two ways to generalize multiple zeta(-star) values, or MZ(S)Vs for short, which are q-analogue and t-interpolation. The q-analogue of MZ(S)Vs, or qMZ(S)Vs for short, was introduced by Bradley, Okuda and Takeyama, Zhao, etc. On the other hand, the polynomials interpolating MZVs and MZSVs using a parameter t were introduced by Yamamoto. We call these t-MZVs.In this paper, we consider such two generalizations simultaneously, that is, we compose polynomials, called t-qMZVs, interpolating qMZVs and qMZSVs using a parameter t which are reduced to q  MZVs as t=0t=0, to q  MZSVs as t=1t=1, and to t  -MZVs as q→1q→1. Then we prove Kawashima type relation, cyclic sum formula and Hoffman type relation for t-qMZVs.