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The Bowman-Bradley theorem for multiple zeta-star values. (English) Zbl 1269.11082

Summary: The Bowman-Bradley theorem asserts that the multiple zeta values at the sequences obtained by inserting a fixed number of two’s between \(3,1,\ldots ,3,1\) 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.

MSC:

11M32 Multiple Dirichlet series and zeta functions and multizeta values
05A19 Combinatorial identities, bijective combinatorics
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