Quasi-shuffle algebras and applications

TL;DR

This paper generalizes key concepts from multiple zeta value theory, such as the interpolated product and symmetric sum theorem, to all quasi-shuffle algebras, broadening their applicability in mathematical research.

Contribution

It extends the interpolated product and symmetric sum theorem from multiple zeta values to general quasi-shuffle algebras, enhancing their theoretical framework.

Findings

Generalization of the interpolated product to all quasi-shuffle algebras

Extension of the symmetric sum theorem beyond multiple zeta values

Broader applicability of quasi-shuffle algebra techniques

Abstract

Quasi-shuffle algebras have been a useful tool in studying multiple zeta values and related quantities, including multiple polylogarithms, finite multiple harmonic sums, and q-multiple zeta values. Here we show that two ideas previously considered only for multiple zeta values, the interpolated product of S. Yamamoto and the symmetric sum theorem, can be generalized to any quasi-shuffle algebra.