On Mordell-Tornheim sums and multiple zeta values

Abstract

We prove that any Mordell-Tornheim sum with positive integer arguments can be expressed as a rational linear combination of multiple zeta values of the same weight and depth. By a result of Tsumura, it follows that any Mordell-Tornheim sum with weight and depth of opposite parity can be expressed as a rational linear combination of products of multiple zeta values of lower depth.

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References in corpus (5)

• Multiple $q$-Zeta Values
• Parametric Euler Sum Identities
• The Algebra and Combinatorics of Shuffles and Multiple Zeta Values
• Signed q-Analogs of Tornheim's Double Series
• Partition Identities for the Multiple Zeta Function

Cited by in corpus (6)

• Multiple zeta-star values and multiple integrals
• Multi-polylogs at twelfth roots of unity and special values of Witten multiple zeta function attached to the exceptional Lie algebra G_2
• Alternating Euler sums and special values of Witten multiple zeta function attached to so(5)
• Finite and symmetric Mordell-Tornheim multiple zeta values
• Depth reduction of a class of Witten zeta functions
• On a unified double zeta function of Mordell--Tornheim type