Multiple q-zeta functions and multiple q-polylogarithms
نویسندگان
چکیده
منابع مشابه
q-Multiple Zeta Functions and q-Multiple Polylogarithms
We shall define the q-analogs of multiple zeta functions and multiple polylogarithms in this paper and study their properties, based on the work of Kaneko et al. and Schlesinger, respectively.
متن کاملMultiple q-zeta functions and multiple q-polylogarithms
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 C 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 va...
متن کاملMultiple q-Zeta Brackets
The multiple zeta values (MZVs) possess a rich algebraic structure of algebraic relations, which is conjecturally determined by two different (shuffle and stuffle) products of a certain algebra of noncommutative words. In a recent work, Bachmann constructed a q-analogue of the MZVs — the so-called bi-brackets — for which the two products are dual to each other, in a very natural way. We overvie...
متن کاملMultiple q-zeta values
We introduce a q-analog of the multiple harmonic series commonly referred to as multiple zeta values. The multiple q-zeta values satisfy a q-stuffle multiplication rule analogous to the stuffle multiplication rule arising from the series representation of ordinary multiple zeta values. Additionally, multiple q-zeta values can be viewed as special values of the multiple q-polylogarithm, which ad...
متن کاملSome remarks on q-deformed multiple polylogarithms
We introduce general q-deformed multiple polylogarithms which even in the dilogarithm case differ slightly from the deformation usually discussed in the literature. The merit of the deformation as suggested, here, is that q-deformed multiple polylogarithms define an algebra, then (as in the undeformed case). For the special case of qdeformed multiple ζ-values, we show that there exists even a n...
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ژورنال
عنوان ژورنال: The Ramanujan Journal
سال: 2007
ISSN: 1382-4090,1572-9303
DOI: 10.1007/s11139-007-9025-9