Multiple q-zeta functions and multiple q-polylogarithms

By Jianqiang Zhao. 2003

93 citations recorded by the source corpus.

Abstract For every positive integer d we define the q-analog of multiple zeta function of depth d and study its properties, generalizing the work of Kaneko et al. who dealt with the case d=1. We first analytically continue it to a meromorphic function on ℂd with explicit poles. In our Main Theorem we show that its limit when q↑1 is the ordinary multiple zeta function. Then we consider some special values of these functions when d=2. At the end of the paper we also propose the q-analogs of multiple polylogarithms by using Jackson’s q-iterated integrals and then study some of their properties. Our definition is motivated by those of Koornwinder and Schlesinger although theirs are slightly different from ours.

Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics

View Paper: https://www.semanticscholar.org/paper/3d78304f283a58b1602700ec04bd52a81c367ade

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In Algebra and Number Theory

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Citations in the corpus

On relations for the multiple q-zeta values (2007, methodology): “In this paper we prove some relations for a certain class of q-series called qmultiple zeta values (qMZV, for short). Let us recall the definition of qMZV [ 10 ].”
Multiple $q$-Zeta Values (2004, methodology): “Remark 5. Zhao [ 27 ] has outlined an alternative approach to deriving the multiple Jackson q-integral representation of the multiple q-polylogarithm.”
The algebra of generating functions for multiple divisor sums and applications to multiple zeta values (2013, methodology): “MZV due to the limiting process. It seems strange to us, that albeit the cases (1−q)s[s] have been treated as q-zeta values [Zu], [Pu] or [KKW] the deﬁnition (6.1) has become standard (see e.g. [Br], [Zh],[OKZ]) and not (1− q)s1+,...,s k[s 1,...,sl]. Remark 6.2. There is also another q-analogue, whi”