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A polynomial basis for the multizeta algebra in positive characteristic
Abstract
Let K=𝔽q(θ), and let 𝒵 be the K-algebra generated by Thakur's multiple zeta values ζA(s). We prove that 𝒵 is a polynomial algebra and construct an explicit polynomial basis of 𝒵 over K. We also determine the transcendence degree of K[ζA(s): wt(s) leqslant w] over K for every integer w geqslant 1, generalizing a result of Ngo Dac--Nguyen Chu--Pham. The proof uses Chang's grading theorem, the linear basis theorem proved independently by Chang--Chen--Mishiba and Im--Kim--Le--Ngo Dac--Pham, and the carry relations of Im--Kim--Ngo Dac. The key step is to show that suitable derivations obtained from deconcatenation and linear functionals descend through the carry relations to 𝒵.
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BibTeX
@misc{lai2026polynomial,
title = {{A polynomial basis for the multizeta algebra in positive characteristic}},
author = {Li Lai},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.24773},
eprint = {2609.24773},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.24773},
}
RIS
TY - UNPB
TI - A polynomial basis for the multizeta algebra in positive characteristic
AU - Li Lai
PY - 2026
DA - 2026/09/21
PB - arXiv
DO - 10.48550/arxiv.2609.24773
UR - https://arxiv.org/abs/2609.24773
AB - Let K=𝔽_q(θ), and let 𝒵 be the K-algebra generated by Thakur's multiple zeta values ζ_A(s). We prove that 𝒵 is a polynomial algebra and construct an explicit polynomial basis of 𝒵 over K. We also determine the transcendence degree of K[ζ_A(s): wt(s) leqslant w] over K for every integer w geqslant 1, generalizing a result of Ngo Dac--Nguyen Chu--Pham. The proof uses Chang's grading theorem, the linear basis theorem proved independently by Chang--Chen--Mishiba and Im--Kim--Le--Ngo Dac--Pham, and the carry relations of Im--Kim--Ngo Dac. The key step is to show that suitable derivations obtained from deconcatenation and linear functionals descend through the carry relations to 𝒵.
ER -