Reducibility of Signed Cyclic Sums of Mordell-Tornheim Zeta and L-Values

TL;DR

This paper demonstrates that specific signed cyclic sums of Mordell-Tornheim L-values can be expressed as rational linear combinations of products of lower-depth multiple L-values, generalizing previous results and proving reducibility of certain sums.

Contribution

It introduces a new reducibility result for signed cyclic sums of Mordell-Tornheim L-values, extending prior work and establishing reducibility for sums with repeated arguments.

Findings

Signed cyclic sums are rational linear combinations of lower-depth products.

Mordell-Tornheim sums with repeated arguments are reducible.

Generalizes previous results by Subbarao, Sitaramachandrarao, and Matsumoto et al.

Abstract

In this paper, we shall show that certain signed cyclic sums of Mordell-Tornheim L-values are rational linear combinations of products of multiple L-values of lower depths (i.e., reducible). This simultaneously generalizes some results of Subbarao and Sitaramachandrarao, and Matsumoto et al. As a direct corollary, we can prove that for any integer k>2 and positive integer n, the Mordell-Tornheim sums zeta_\MT(\{n\}_k) is reducible.