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Multiple $q$-zeta brackets (1412.0163v2)
Published 29 Nov 2014 in math.NT, math-ph, and math.MP
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.