PreprintCC BY 4.0arXiv
Mishiba's Conjecture on the Coaction of ∞-adic Multiple Zeta Values
Abstract
We study multiple zeta values in positive characteristic. We construct, using ∞-adic multiple zeta values, a coaction of the ∞-adic multiple zeta value algebra modulo ζA(q−1) on the ∞-adic multiple zeta value algebra itself, and prove that it agrees with Mishiba's coaction constructed via special values of Carlitz multiple polylogarithms. We also determine the coaction on the ⋆-inverse values and show that the antipode on the ∞-adic multiple zeta value algebra modulo ζA(q−1) is given by the ⋆-inverse operation. In particular, these results prove Mishiba's conjecture concerning the coaction and the antipode for ∞-adic multiple zeta values.
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BibTeX
@misc{tsui2026mishibas,
title = {{Mishiba's Conjecture on the Coaction of $\infty$-adic Multiple Zeta Values}},
author = {Hung-Chun Tsui},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.30823},
eprint = {2609.30823},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.30823},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Mishiba's Conjecture on the Coaction of ∞-adic Multiple Zeta Values
AU - Hung-Chun Tsui
PY - 2026
DA - 2026/09/25
PB - arXiv
DO - 10.48550/arxiv.2609.30823
UR - https://arxiv.org/abs/2609.30823
AB - We study multiple zeta values in positive characteristic. We construct, using ∞-adic multiple zeta values, a coaction of the ∞-adic multiple zeta value algebra modulo ζ_A(q−1) on the ∞-adic multiple zeta value algebra itself, and prove that it agrees with Mishiba's coaction constructed via special values of Carlitz multiple polylogarithms. We also determine the coaction on the ⋆-inverse values and show that the antipode on the ∞-adic multiple zeta value algebra modulo ζ_A(q−1) is given by the ⋆-inverse operation. In particular, these results prove Mishiba's conjecture concerning the coaction and the antipode for ∞-adic multiple zeta values.
ER -