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PreprintCC BY 4.0arXiv

Multiple Zeta Values in Positive Characteristic: A Kaneko-Zagier-Type Conjecture

  • Hung-Chun Tsui
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Abstract

In this paper, we study a comparison between ∞-adic and finite multiple zeta values in positive characteristic. We construct a surjective comparison map from the algebra of ∞-adic multiple zeta values to a quotient of the algebra of finite multiple zeta values. This map factors through the quotient by ζA(q−1), thereby establishing the well-definedness of a Kaneko-Zagier-type conjectural map. We further show that the comparison map is compatible with special values of Carlitz multiple polylogarithms, as well as with the corresponding ⋆-inverse values. As an application, we prove the upper bound predicted by Shi's dimension conjecture for finite multiple zeta values.

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Cite

BibTeXRIS
BibTeX
@misc{tsui2026multiple,
  title = {{Multiple Zeta Values in Positive Characteristic: A Kaneko-Zagier-Type Conjecture}},
  author = {Hung-Chun Tsui},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.37450},
  eprint = {2609.37450},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.37450},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Multiple Zeta Values in Positive Characteristic: A Kaneko-Zagier-Type Conjecture
AU  - Hung-Chun Tsui
PY  - 2026
DA  - 2026/09/26
PB  - arXiv
DO  - 10.48550/arxiv.2609.37450
UR  - https://arxiv.org/abs/2609.37450
AB  - In this paper, we study a comparison between ∞-adic and finite multiple zeta values in positive characteristic. We construct a surjective comparison map from the algebra of ∞-adic multiple zeta values to a quotient of the algebra of finite multiple zeta values. This map factors through the quotient by ζ_A(q−1), thereby establishing the well-definedness of a Kaneko-Zagier-type conjectural map. We further show that the comparison map is compatible with special values of Carlitz multiple polylogarithms, as well as with the corresponding ⋆-inverse values. As an application, we prove the upper bound predicted by Shi's dimension conjecture for finite multiple zeta values.
ER  -