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BOWMAN-BRADLEY TYPE THEOREM FOR FINITE MULTIPLE ZETA VALUES IN A₂

Murahara, Hideki 大阪大学 DOI:10.18910/76677

2020.07

概要

Bowman and Bradley obtained a remarkable formula among multiple zeta values. The formula states that the sum of multiple zeta values for indices which consist of the shuffle of two kinds of the strings {1, 3, . . . , 1, 3} and {2, . . . , 2} is a rational multiple of a power of π². Recently, Saito and Wakabayashi proved that analogous but more general sums of finite multiple zeta values in an adelic ring A₁ vanish. In this paper, we partially lift Saito-Wakabayashi’s theorem from A₁ to A₂. Our result states that a Bowman-Bradley type sum of finite multiple zeta values in A₂ is a rational multiple of a special element and this is closer to the original Bowman-Bradley theorem.

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参考文献

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