The Bowman-Bradley theorem for multiple zeta-star values

TL;DR

This paper proves a new identity for multiple zeta-star values, extending the Bowman-Bradley theorem, by using non-commutative algebra techniques to show these sums relate to powers of pi.

Contribution

It establishes the Bowman-Bradley theorem's counterpart for multiple zeta-star values through algebraic identities, advancing understanding of these special number sequences.

Findings

Proves the Bowman-Bradley theorem for multiple zeta-star values.

Uses Hoffman’s non-commutative polynomial algebra to establish the identity.

Shows the sum of specific multiple zeta-star values is a rational multiple of a power of pi.

Abstract

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 establish its counterpart for multiple zeta-star values by showing an identity in a non-commutative polynomial algebra introduced by Hoffman.