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Confluence relations, Hoffman basis over \mathbb{Z}_{(2)}, and the Deligne--Drinfeld conjecture
Abstract
We express every admissible word as a ℤ(2)-linear combination of Hoffman words and explicit confluence relations. This implies that every multiple zeta value is a linear combination of elements of the Hoffman basis with coefficients having odd denominators, as conjectured by Hirose and Sato. Combined with Brown's theorem and Furusho's characterization of the Grothendieck--Teichmüller group GRT by confluence relations, our result identifies the de Rham motivic Galois group of mixed Tate motives over ℤ with GRT and gives an alternative proof of the Deligne--Drinfeld conjecture, for which a proof was previously presented in the OpenAI Math Release.
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BibTeX
@misc{hirose2026confluence,
title = {{Confluence relations, Hoffman basis over \mathbbZ_(2), and the Deligne--Drinfeld conjecture}},
author = {Minoru Hirose},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.23719},
eprint = {2610.23719},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.23719},
}
RIS
TY - UNPB
TI - Confluence relations, Hoffman basis over \mathbb{Z}_{(2)}, and the Deligne--Drinfeld conjecture
AU - Minoru Hirose
PY - 2026
DA - 2026/10/16
PB - arXiv
DO - 10.48550/arxiv.2610.23719
UR - https://arxiv.org/abs/2610.23719
AB - We express every admissible word as a ℤ_(2)-linear combination of Hoffman words and explicit confluence relations. This implies that every multiple zeta value is a linear combination of elements of the Hoffman basis with coefficients having odd denominators, as conjectured by Hirose and Sato. Combined with Brown's theorem and Furusho's characterization of the Grothendieck--Teichmüller group GRT by confluence relations, our result identifies the de Rham motivic Galois group of mixed Tate motives over ℤ with GRT and gives an alternative proof of the Deligne--Drinfeld conjecture, for which a proof was previously presented in the OpenAI Math Release.
ER -