Vol. 303, No. 1, 2019

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Restricted sum formula for finite and symmetric multiple zeta values

Hideki Murahara and Shingo Saito

Vol. 303 (2019), No. 1, 325–335

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.

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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
Received: 8 January 2018
Revised: 10 October 2018
Accepted: 20 April 2019
Published: 21 December 2019
Hideki Murahara
Nakamura Gakuen University Graduate School
Befu, Jonan-ku
Shingo Saito
Faculty of Arts and Science
Kyushu University
Motooka, Nishi-ku