Tohoku Mathematical Journal
2021
June
SECOND SERIES VOL. 73, NO. 2

Tohoku Math. J.
73 (2021), 221-255

Title FINITE MULTIPLE ZETA VALUES, SYMMETRIC MULTIPLE ZETA VALUES AND UNIFIED MULTIPLE ZETA FUNCTIONS

Author Yasushi Komori

(Received July 22, 2019, revised February 20, 2020)
Abstract. We introduce entire multiple zeta functions, which are natural interpolations of symmetric multiple zeta values. Moreover we give further generalizations which interpolate these zeta functions, $\widehat{\mathcal{A}}$-finite multiple zeta values and $\widehat{\mathcal{S}}$-symmetric multiple zeta values. We also show that the correspondence which Kaneko--Zagier conjecture suggests holds on nonpositive integers for finite multiple zeta values and special values of these multiple zeta functions.

Mathematics Subject Classification. Primary 11M32; Secondary 11M35.
Key words and phrases. Finite multiple zeta values, symmetric multiple zeta values, multiple zeta functions.

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