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

被引:5
作者
Wakabayashi, Noriko [1 ]
机构
[1] Ritsumeikan Univ, Coll Sci & Engn, 1-1-1 Nojihigashi, Kusatsu, Shiga 5258577, Japan
基金
日本学术振兴会;
关键词
t-qMZVs; Harmonic products; Kawashima type relation; Cyclic sum formula; Hoffman type relation;
D O I
10.1016/j.jnt.2016.10.007
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
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 -> 1. Then we prove Kawashima type relation, cyclic sum formula and Hoffman type relation for t-qMZVs. (C) 2016 Elsevier Inc. All rights reserved.
引用
收藏
页码:26 / 39
页数:14
相关论文
共 10 条
[1]   Multiple q-zeta values [J].
Bradley, DM .
JOURNAL OF ALGEBRA, 2005, 283 (02) :752-798
[2]   The algebra of multiple harmonic series [J].
Hoffman, ME .
JOURNAL OF ALGEBRA, 1997, 194 (02) :477-495
[3]   On the sum formula for the q-analogue of non-strict multiple zeta values [J].
Ohno, Yasuo ;
Okuda, Jun-Ichi .
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2007, 135 (10) :3029-3037
[4]   On relations for the multiple q-zeta values [J].
Okuda, Jun-ichi ;
Takeyama, Yoshihiro .
RAMANUJAN JOURNAL, 2007, 14 (03) :379-387
[5]   Quadratic relations for a q-analogue of multiple zeta values [J].
Takeyama, Yoshihiro .
RAMANUJAN JOURNAL, 2012, 27 (01) :15-28
[6]   Kawashima's relations for interpolated multiple zeta values [J].
Tanaka, Tatsushi ;
Wakabayashi, Noriko .
JOURNAL OF ALGEBRA, 2016, 447 :424-431
[7]   An algebraic proof of the cyclic sum formula for multiple zeta values [J].
Tanaka, Tatsushi ;
Wakabayashi, Noriko .
JOURNAL OF ALGEBRA, 2010, 323 (03) :766-778
[8]  
Wakabayashi N., INT J NUMBER THEORY
[9]   Interpolation of multiple zeta and zeta-star values [J].
Yamamoto, Shuji .
JOURNAL OF ALGEBRA, 2013, 385 :102-114
[10]   Multiple q-zeta functions and multiple q-polylogarithms [J].
Zhao, Jianqiang .
RAMANUJAN JOURNAL, 2007, 14 (02) :189-221