Multiple q-Zeta Brackets

Mathematics

Wadim Zudilin¹ 

[1] School of Mathematical and Physical Sciences, the University of Newcastle, Callaghan, NSW 2308, Australia; E-Mail

关键词: multiple zeta value;    q-analogue;    multiple divisor sum;    double shuffle relations;    linear independence;    radial asymptotics;   

DOI  :  10.3390/math3010119

来源: mdpi

【 摘 要 】

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.

【 授权许可】

CC BY   
© 2015 by the authors; licensee MDPI, Basel, Switzerland