On the structure of Multiple q-Zeta Values
Number Theory
2025-11-11 v1 Combinatorics
Abstract
In 2015, Bachmann \cite{Ba3} conjectured that the~-vector space~ of (formal)~-analogues of Multiple Zeta Values (\qmzv s) is spanned by a very particular set compared to known spanning sets. In this work, we prove that this conjecture is true for a subspace of~ spanned by words satisfying some condition on their number of zeros and depth. According to this partial result, we give an explicit approach to the whole conjecture, based on particular~-linear relations among formal Multiple~-Zeta Values which are implied by duality.
Cite
@article{arxiv.2511.07302,
title = {On the structure of Multiple q-Zeta Values},
author = {Benjamin Brindle},
journal= {arXiv preprint arXiv:2511.07302},
year = {2025}
}
Comments
Comments welcome! In particular, comments about the 'box product' and whether it occurs somewhere else already would be great!