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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, \({}_r\phi_s\)
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