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PreprintCC BY 4.0arXiv

A generating function identity for finite and symmetric multiple zeta values via Dougall's bilateral 2H2 summation

  • Takumi Maesaka
  • Masataka Ono
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Abstract

We establish a generating function identity for finite and symmetric multiple zeta values using Dougall's bilateral 2H2 summation formula. As an application, we prove a restricted sum formula in which the parity of each component of the index is prescribed. We also derive a generating function identity for finite multiple zeta values ζ𝒜({1,2}n) and symmetric multiple zeta values ζ𝒮({1,2}n), thereby proving Kaneko's conjecture for finite multiple zeta values and its symmetric analogue.

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Cite

BibTeXRIS
BibTeX
@misc{maesaka2026generating,
  title = {{A generating function identity for finite and symmetric multiple zeta values via Dougall's bilateral $_2H_2$ summation}},
  author = {Takumi Maesaka and Masataka Ono},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.17957},
  eprint = {2610.17957},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.17957},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - A generating function identity for finite and symmetric multiple zeta values via Dougall's bilateral _2H_2 summation
AU  - Takumi Maesaka
AU  - Masataka Ono
PY  - 2026
DA  - 2026/10/13
PB  - arXiv
DO  - 10.48550/arxiv.2610.17957
UR  - https://arxiv.org/abs/2610.17957
AB  - We establish a generating function identity for finite and symmetric multiple zeta values using Dougall's bilateral _2H_2 summation formula. As an application, we prove a restricted sum formula in which the parity of each component of the index is prescribed. We also derive a generating function identity for finite multiple zeta values ζ^_𝒜({1,2}^n) and symmetric multiple zeta values ζ^_𝒮({1,2}^n), thereby proving Kaneko's conjecture for finite multiple zeta values and its symmetric analogue.
ER  -