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

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