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

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

2009-04-06

arxiv.org/abs/0904.0888v2

J. of Alg. and Its Applications, 9 (2010), pp. 327-337

Mathematics

Number Theory

10 pages, more examples are included

Scientific paper

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.

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