Multiple q-Zeta Brackets
School of Mathematical and Physical Sciences, the University of Newcastle, Callaghan, NSW 2308, Australia
Academic Editor: Palle Jorgensen
Mathematics 2015, 3(1), 119-130; https://doi.org/10.3390/math3010119
Received: 27 January 2015 / Accepted: 13 March 2015 / Published: 20 March 2015
(This article belongs to the Special Issue Mathematical physics)
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
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MDPI and ACS Style
Zudilin, W. Multiple q-Zeta Brackets. Mathematics 2015, 3, 119-130.
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Zudilin W. Multiple q-Zeta Brackets. Mathematics. 2015; 3(1):119-130.Chicago/Turabian Style
Zudilin, Wadim. 2015. "Multiple q-Zeta Brackets." Mathematics 3, no. 1: 119-130.
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