Quasi-shuffle products revisited

Abstract

Quasi-shuffle products, introduced by the first author, have been useful in studying multiple zeta values and some of their analogues and generalizations. The second author, together with Kajikawa, Ohno, and Okuda, significantly extended the definition of quasi-shuffle algebras so it could be applied to multiple zeta q-values. This article extends some of the algebraic machinery of the first author's original paper to the more general definition, and uses this extension to obtain various algebraic formulas in the quasi-shuffle algebra in a transparent way. Some applications to multiple zeta values, interpolated multiple zeta values, multiple q-zeta values, and multiple polylogarithms are given.

This is an extensively revised and expanded version of the Max Planck Institute preprint (MPIM 2012-16) with the same title. 27 Oct 16: minor revision and corrections 3 Apr 17: additional revision and corrections

References in corpus (2)

• Quasi-shuffle products revisited
• The Hopf algebra structure of multiple harmonic sums

Cited by in corpus (22)

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• Quasi-shuffle algebras and renormalisation of rough differential equations
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• Duality and (q-)multiple zeta values
• Apéry-Type Series and Colored Multiple Zeta Values
• The Hopf algebras of signed permutations, of weak quasi-symmetric functions and of Malvenuto-Reutenauer
• Generalized iterated-sums signatures
• Quasi-geometric rough paths and rough change of variable formula
• Algebraic relations of interpolated multiple zeta values
• Symmetry results for multiple $t$-values
• Balanced multiple q-zeta values
• A generalization of formal multiple zeta values related to multiple Eisenstein series and multiple q-zeta values
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• Formal multiple Eisenstein series and their derivations
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• Complete families of embedded high genus CMC surfaces in the 3-sphere (with an appendix by Steven Charlton)
• Generalized Matsumoto-Tits sections and quantum quasi-shuffle algebras