Vol. 286, No. 2, 2017

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Identities involving cyclic and symmetric sums of regularized multiple zeta values

Tomoya Machide

Vol. 286 (2017), No. 2, 307–359

There are two types of regularized multiple zeta values: harmonic and shuffle types. The first purpose of the present paper is to give identities involving cyclic sums of regularized multiple zeta values of both types for depth less than 5. Michael Hoffman, in “Quasi-symmetric functions and mod p multiple harmonic sums” (Kyushu Journal of Mathematics 69 (2015), 345–366) proved an identity involving symmetric sums of regularized multiple zeta values of harmonic type for arbitrary depth. The second purpose is to prove Hoffman’s identity for shuffle type. We also give a connection between the identities involving cyclic sums and symmetric sums, for depth less than 5.

multiple zeta value, cyclic sum, symmetric sum, group ring of symmetric group
Mathematical Subject Classification 2010
Primary: 11M32
Secondary: 16S34, 20C05
Received: 15 December 2014
Revised: 17 December 2015
Accepted: 14 January 2016
Published: 15 January 2017
Tomoya Machide
JST, ERATO, Kawarabayashi Large Graph Project
Global Research Center for Big Data Mathematics
National Institute of Informatics
2-1-2 Hitotsubashi
Tokyo 101-8430