Tohoku Mathematical Journal
2022
September
SECOND SERIES VOL. 74, NO. 3

Tohoku Math. J.
74 (2022), 399-428

Title GENERATING FUNCTIONS FOR SUMS OF POLYNOMIAL MULTIPLE ZETA VALUES

Author Minoru Hirose, Hideki Murahara and Shingo Saito

(Received November 30, 2020, revised April 7, 2021)
Abstract. The sum formulas for multiple zeta(-star) values and symmetric multiple zeta(-star) values bear a striking resemblance. We explain the resemblance in a rather straightforward manner using an identity that involves the Schur multiple zeta values. We also obtain the sum formula for polynomial multiple zeta(-star) values in terms of generating functions, simultaneously generalizing the sum formulas for multiple zeta(-star) values and symmetric multiple zeta(-star) values.

Mathematics Subject Classification. Primary 11M32; Secondary 05A19.
Key words and phrases. Multiple zeta(-star) values, symmetric multiple zeta(-star) values, polynomial multiple zeta(-star) values, sum formula.

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