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Duality formulas for 𝒬̂-multiple zeta values

  • Koki Ishida
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Abstract

In this paper, we introduce two duality formulas for 𝒬̂-multiple zeta values (𝒬̂-MZVs for short) which are defined by Takeyama and Tasaka. Since taking two different limits of 𝒬̂-MZV recovers the p-adic multiple zeta value and the t-adic multiple zeta value respectively, finding the relation of 𝒬̂-MZVs partially supports the Kaneko--Zagier conjecture and its refined version. Currently, three types of duality formulas for the p-adic multiple zeta values are known, and for one of them, the q-analogue was studied by Takeyama and Tasaka. We present q-analogues of the remaining two duality formulas for the p-adic multiple zeta values.

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Cite

BibTeXRIS
BibTeX
@misc{ishida2026duality,
  title = {{Duality formulas for $\widehat\mathcalQ$-multiple zeta values}},
  author = {Koki Ishida},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2608.12041},
  eprint = {2608.12041},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.12041},
}
RIS
TY  - UNPB
TI  - Duality formulas for 𝒬̂-multiple zeta values
AU  - Koki Ishida
PY  - 2026
DA  - 2026/10/19
PB  - arXiv
DO  - 10.48550/arxiv.2608.12041
UR  - https://arxiv.org/abs/2608.12041
AB  - In this paper, we introduce two duality formulas for 𝒬̂-multiple zeta values (𝒬̂-MZVs for short) which are defined by Takeyama and Tasaka. Since taking two different limits of 𝒬̂-MZV recovers the p-adic multiple zeta value and the t-adic multiple zeta value respectively, finding the relation of 𝒬̂-MZVs partially supports the Kaneko--Zagier conjecture and its refined version. Currently, three types of duality formulas for the p-adic multiple zeta values are known, and for one of them, the q-analogue was studied by Takeyama and Tasaka. We present q-analogues of the remaining two duality formulas for the p-adic multiple zeta values.
ER  -