Duality and (q-)multiple zeta values

Abstract

Following Bachmann's recent work on bi-brackets and multiple Eisenstein series, Zudilin introduced the notion of multiple q-zeta brackets, which provides a q-analog of multiple zeta values possessing both shuffle as well as quasi-shuffle relations. The corresponding products are related in terms of duality. In this work we study Zudilin's duality construction in the context of classical multiple zeta values as well as various q-analogs of multiple zeta values. Regarding the former we identify the derivation relation of order two with a Hoffman-Ohno type relation. Then we describe relations between the Ohno-Okuda-Zudilin q-multiple zeta values and the Schlesinger-Zudilin q-multiple zeta values.

arXiv commentrevised version, accepted for publication in Advances in Mathematics

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Cited by in corpus (3)

• Multiple zeta values and Euler sums
• A generalization of formal multiple zeta values related to multiple Eisenstein series and multiple q-zeta values
• Balanced multiple q-zeta values