## Tohoku Mathematical Journal 2016 June SECOND SERIES VOL. 68, NO. 2

 Tohoku Math. J. 68 (2016), 241-251

Title BOWMAN-BRADLEY TYPE THEOREM FOR FINITE MULTIPLE ZETA VALUES

Author Shingo Saito and Noriko Wakabayashi

(Received July 2, 2014, revised October 1, 2014)
Abstract. The multiple zeta values are multivariate generalizations of the values of the Riemann zeta function at positive integers. The Bowman-Bradley theorem asserts that the multiple zeta values at the sequences obtained by inserting a fixed number of twos between $3,1,\dots,3,1$ add up to a rational multiple of a power of $\pi$. We show that an analogous theorem holds in a very strong sense for finite multiple zeta values, which have been investigated by Hoffman and Zhao among others and recently recast by Zagier.

Mathematics Subject Classification. Primary 11M32; Secondary 05A19.

Key words and phrases. Finite multiple zeta value, Bowman-Bradley theorem.