Restricted sum formula for finite and symmetric multiple zeta values

Hideki Murahara and Shingo Saito

Vol. 303 (2019), No. 1, 325–335

DOI: 10.2140/pjm.2019.303.325

Abstract

The sum formula for finite and symmetric multiple zeta values, established by Wakabayashi and the authors, implies that if the weight and depth are fixed and the specified component is required to be more than one, then the values sum up to a rational multiple of the analogue of the Riemann zeta value. We prove that the result remains true if we further demand that the component should be more than two or that another component should also be more than one.

Keywords

finite multiple zeta values, symmetric multiple zeta values, symmetrised multiple zeta values, finite real multiple zeta values, sum formula, restricted sum formula

Mathematical Subject Classification 2010

Primary: 11M32

Secondary: 05A19

Milestones

Received: 8 January 2018

Revised: 10 October 2018

Accepted: 20 April 2019

Published: 21 December 2019