2016/09/05 by Wakabayashi, Noriko
#FOS: Mathematics #Number Theory (math.NT)
paper · doi:10.48550/arxiv.1609.01197
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 qMZVs as t=0, to qMZSVs as t=1, and to t-MZVs as q tends to 1. Then we prove Kawashima type relation, cyclic sum formula and Hoffman type relation for t-qMZVs.