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Mathematics 2015, 3(1), 119-130; doi:10.3390/math3010119

Multiple q-Zeta Brackets

School of Mathematical and Physical Sciences, the University of Newcastle, Callaghan, NSW 2308, Australia
Academic Editor: Palle Jorgensen
Received: 27 January 2015 / Accepted: 13 March 2015 / Published: 20 March 2015
(This article belongs to the Special Issue Mathematical physics)
View Full-Text   |   Download PDF [221 KB, uploaded 20 March 2015]

Abstract

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 overview Bachmann’s construction and discuss the radial asymptotics of the bi-brackets, its links to the MZVs, and related linear (in)dependence questions of the q-analogue. View Full-Text
Keywords: multiple zeta value; q-analogue; multiple divisor sum; double shuffle relations; linear independence; radial asymptotics multiple zeta value; q-analogue; multiple divisor sum; double shuffle relations; linear independence; radial asymptotics
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Zudilin, W. Multiple q-Zeta Brackets. Mathematics 2015, 3, 119-130.

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