PreprintCC BY 4.0arXiv
Quasi-modularity of symmetric quasi-shuffles
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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BibTeX
@misc{hongminh2026quasimodularity,
title = {{Quasi-modularity of symmetric quasi-shuffles}},
author = {Killian Hong-Minh and Sergey Mozgovoy},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.10309},
eprint = {2609.10309},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.10309},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Quasi-modularity of symmetric quasi-shuffles
AU - Killian Hong-Minh
AU - Sergey Mozgovoy
PY - 2026
DA - 2026/09/09
PB - arXiv
DO - 10.48550/arxiv.2609.10309
UR - https://arxiv.org/abs/2609.10309
AB - 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.
ER -