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

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.

References in corpus (3)

• Standard Relations of Multiple Polylogarithm Values at Roots of Unity
• Multiple polylogarithm values at roots of unity
• Double Shuffle Relations of Euler Sums

Cited by in corpus (1)

• A Note on Colored Tornheim's Double Series