Multi-polylogs at twelfth roots of unity and special values of Witten multiple zeta function attached to the exceptional Lie algebra G_2

Abstract

In this note we shall study the Witten multiple zeta function associated to the exceptional Lie algebra g_2. Our main result shows that its special values at nonnegative integers can always be expressed as rational linear combinations of the multi-polylogs evaluated at 12th roots of unity, except for two irregular cases.

10 pages, more examples are included

References in corpus (7)

• Mean value theorems for the double zeta-function
• Standard Relations of Multiple Polylogarithm Values at Roots of Unity
• On Witten multiple zeta-functions associated with semisimple Lie algebras III
• Multiple polylogarithm values at roots of unity
• On Mordell-Tornheim sums and multiple zeta values
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Cited by in corpus (3)

• On Witten multiple zeta-functions associated with semisimple Lie algebras III
• On Witten multiple zeta-functions associated with semisimple Lie algebras IV
• Witten volume formulas for semi-simple Lie algebras