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Confluence relations for q-analogues of multiple zeta values
Abstract
In this paper, we construct confluence relations for q-analogues of multiple zeta values by adapting the classical construction to the q-setting. Our construction uses q-analogues of multiple polylogarithms depending on an auxiliary variable z, functional relations arising from their q-differential equations, and the (regularized) limit as z tends to $1$. We prove that the resulting family of relations contains the stuffle product relations and, assuming a certain conjectural identity, the duality relations for both the Bradley--Zhao and Schlesinger--Zudilin models.
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BibTeX
@misc{hirose2026confluence,
title = {{Confluence relations for $q$-analogues of multiple zeta values}},
author = {Minoru Hirose},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.01458},
eprint = {2609.01458},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.01458},
}
RIS
TY - UNPB
TI - Confluence relations for q-analogues of multiple zeta values
AU - Minoru Hirose
PY - 2026
DA - 2026/09/01
PB - arXiv
DO - 10.48550/arxiv.2609.01458
UR - https://arxiv.org/abs/2609.01458
AB - In this paper, we construct confluence relations for q-analogues of multiple zeta values by adapting the classical construction to the q-setting. Our construction uses q-analogues of multiple polylogarithms depending on an auxiliary variable z, functional relations arising from their q-differential equations, and the (regularized) limit as z tends to $1$. We prove that the resulting family of relations contains the stuffle product relations and, assuming a certain conjectural identity, the duality relations for both the Bradley--Zhao and Schlesinger--Zudilin models.
ER -