Multiple \(q\)-zeta brackets. (English) Zbl 1312.11069
Summary: 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, H. 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 [“Generating series of multiple divisor sums and other interesting \(q\)-series”. Talk slides. University of Bristol (2014)]. 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.
MSC:
| 11M32 | Multiple Dirichlet series and zeta functions and multizeta values |
Keywords:
multiple zeta value; \(q\)-analogue; multiple divisor sum; double shuffle relations; linear independence; radial asymptoticsReferences:
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