Bowman-Bradley type theorem for finite multiple zeta values

TL;DR

This paper extends the Bowman-Bradley theorem, originally about multiple zeta values, to finite multiple zeta values, demonstrating a strong analogous property involving sums of these values related to powers of pi.

Contribution

The paper proves a Bowman-Bradley type theorem for finite multiple zeta values, establishing a strong analogue of the classical result in the finite setting.

Findings

Finite multiple zeta values satisfy a Bowman-Bradley type relation.

Sums of finite multiple zeta values at specific sequences are rational multiples of powers of pi.

The result connects finite multiple zeta values with classical zeta value properties.

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,...,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.