English

On the structure of Multiple q-Zeta Values

Number Theory 2025-11-11 v1 Combinatorics

Abstract

In 2015, Bachmann \cite{Ba3} conjectured that the~\Q\Q-vector space~\Zq\Zq of (formal)~qq-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~\Zq\Zq 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~\Q\Q-linear relations among formal Multiple~qq-Zeta Values which are implied by duality.

Keywords

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!