Bowman-bradley type theorem for finite multiple zeta values in A₂

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 ring₁ vanish. In this paper, we partially lift Saito-Wakabayashi’s theorem from₁ to₂. Our result states that a Bowman-Bradley type sum of finite multiple zeta values in₂ is a rational multiple of a special element and this is closer to the original Bowman-Bradley theorem.