On variants of symmetric multiple zeta-star values and the cyclic sum formula

Minoru Hirose, Hideki Murahara, Masataka Ono*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

The t-adic symmetric multiple zeta values were defined by Jarossay, which have been studied as a real analogue of the p-adic finite multiple zeta values. In this paper, we consider the star analogues based on several regularization processes of multiple zeta-star values: harmonic regularization, shuffle regularization, and Kaneko–Yamamoto’s type regularization. We also present the cyclic sum formula for t-adic symmetric multiple zeta(-star) values, which is the counterpart of that for p-adic finite multiple zeta(-star) values obtained by Kawasaki. The proof uses our new relationship that connects the cyclic sum formula for t-adic symmetric multiple zeta-star values and that for the multiple zeta-star values.

Original languageEnglish
JournalRamanujan Journal
DOIs
Publication statusAccepted/In press - 2021
Externally publishedYes

Keywords

  • Cyclic sum formula
  • Finite multiple zeta(-star) values
  • Multiple zeta(-star) values
  • Symmetric multiple zeta(-star) values

ASJC Scopus subject areas

  • Algebra and Number Theory

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