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PreprintCC BY 4.0arXiv

Graded Structures of v-adic Carlitz Multiple Polylogarithms and v-adic Multiple Zeta Values

  • Hung-Chun Tsui
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Abstract

In this paper, we study v-adic Carlitz multiple polylogarithms and v-adic multiple zeta values. We prove that, for every finite place v of 𝔽q(θ), the natural weight gives a graded structure on the algebras generated by these values. Moreover, we show that every 𝔽q(θ)̅-linear relation among these values arises from an 𝔽q(θ)-linear relation. In particular, our results establish a function field analogue of the Furusho-Yamashita direct sum conjecture and extend Chen's work from finite places of degree one to arbitrary finite places.

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Cite

BibTeXRIS
BibTeX
@misc{tsui2026graded,
  title = {{Graded Structures of $v$-adic Carlitz Multiple Polylogarithms and $v$-adic Multiple Zeta Values}},
  author = {Hung-Chun Tsui},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.25063},
  eprint = {2610.25063},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.25063},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Graded Structures of v-adic Carlitz Multiple Polylogarithms and v-adic Multiple Zeta Values
AU  - Hung-Chun Tsui
PY  - 2026
DA  - 2026/10/18
PB  - arXiv
DO  - 10.48550/arxiv.2610.25063
UR  - https://arxiv.org/abs/2610.25063
AB  - In this paper, we study v-adic Carlitz multiple polylogarithms and v-adic multiple zeta values. We prove that, for every finite place v of 𝔽_q(θ), the natural weight gives a graded structure on the algebras generated by these values. Moreover, we show that every 𝔽_q(θ)̅-linear relation among these values arises from an 𝔽_q(θ)-linear relation. In particular, our results establish a function field analogue of the Furusho-Yamashita direct sum conjecture and extend Chen's work from finite places of degree one to arbitrary finite places.
ER  -