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arXiv · 2609.10309

Quasi-modularity of symmetric quasi-shuffles

Killian Hong-Minh·Sergey Mozgovoy
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Abstract

We develop an algebraic framework for the quasi-modularity of symmetric multiple $q$-zeta values. We identify natural classes of symmetric quasi-shuffles whose $q$-zeta values exhaust the algebra of level-one quasi-modular forms, and further classes whose $q$-zeta values are quasi-modular forms of finite level. We also obtain explicit symmetrization formulas and relate symmetric quasi-shuffles to symmetric and quasisymmetric functions.

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BibTeXRIS

Killian Hong-Minh, Sergey Mozgovoy. 2026-09-09. Quasi-modularity of symmetric quasi-shuffles. https://arxiv.org/abs/2609.10309

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