Pure and Applied Mathematics Quarterly

Volume 19 (2023)

Number 1

Special Issue in honor of Don Zagier

Guest editors: Benedict H. Gross, Ken Ono, and Fernando Rodriguez Villegas

On finite multiple zeta values of level two

Pages: 267 – 280

DOI: https://dx.doi.org/10.4310/PAMQ.2023.v19.n1.a10


Masanobu Kaneko (Faculty of Mathematics, Kyushu University, Nishi-ku, Fukuoka, Japan)

Takuya Murakami (Sophia Fukuoka Junior and Senior High School, Chuo-ku, Fukuoka, Japan)

Amane Yoshihara (Saitama, Japan)


We introduce and study a “level two” analogue of finite multiple zeta values.We give conjectural bases of the space of finite Euler sums as well as that of usual finite multiple zeta values in terms of these newly defined elements. A kind of “parity result” and certain sum formulas are also presented.


multiple zeta values, finite multiple zeta values, finite Euler sums

2010 Mathematics Subject Classification

Primary 11M32. Secondary 11A07.

This work was supported by JSPS KAKENHI Grant Numbers JP16H06336 and JP21H04430.

Received 1 September 2021

Accepted 27 February 2022

Published 3 April 2023