## On relations for the multiple $$q$$-zeta values.(English)Zbl 1211.11099

Summary: We prove a new relation for the multiple $$q$$-zeta values (M$$q$$ZV’s). It is a $$q$$-analogue of the Ohno-Zagier relation for the multiple zeta values (MZV’s). We discuss the problem of determining the dimension of the space spanned by M$$q$$ ZV’s over $$\mathbb Q$$, and present an application to MZV.

### MSC:

 11M32 Multiple Dirichlet series and zeta functions and multizeta values 11B65 Binomial coefficients; factorials; $$q$$-identities 33D15 Basic hypergeometric functions in one variable, $${}_r\phi_s$$

### Keywords:

Multiple zeta values
Full Text:

### References:

 [1] Bradley, D.M.: Multiple q-zeta values. J. Algebra 283(2), 752–798 (2005). Preprint: February 6, 2004, http://arxiv.org/abs/math.QA/0402093 · Zbl 1114.11075 [2] Gasper, G., Rahman, M.: Basic Hypergeometric Series. Encyclopedia of Mathematics and its Applications, vol. 35. Cambridge University Press, Cambridge (1990). With a foreword by Richard Askey · Zbl 0695.33001 [3] Hoffman, M.E., Ohno, Y.: Relations of multiple zeta values and their algebraic expression. J. Algebra 262(2), 332–347 (2003) · Zbl 1139.11322 [4] Kaneko, M.: Private communications (2004) [5] Ohno, Y.: A generalization of the duality and sum formulas on the multiple zeta values. J. Number Theory 74(1), 39–43 (1999) · Zbl 0920.11063 [6] Ohno, Y., Zagier, D.: Multiple zeta values of fixed weight, depth, and height. Indag. Math. (N.S.) 12(4), 483–487 (2001) · Zbl 1031.11053 [7] Terasoma, T.: Mixed Tate motives and multiple zeta values. Invent. Math. 149(2), 339–369 (2002) · Zbl 1042.11043 [8] Zagier, D.: Values of zeta functions and their applications. In: First European Congress of Mathematics, vol. II, Paris, 1992. Progr. Math., vol. 120, pp. 497–512. Birkhäuser, Basel (1994) · Zbl 0822.11001 [9] Zhao, J.: q-Multiple zeta functions and q-multiple polylogarithms. Preprint, May 23 (2003). http://arxiv.org/abs/math.QA/0304448 · Zbl 1200.11065
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.