MULTI-POLYLOGS AT TWELFTH ROOTS OF UNITY AND SPECIAL VALUES OF WITTEN MULTIPLE ZETA FUNCTION ATTACHED TO THE EXCEPTIONAL LIE ALGEBRA 𝔤2-Reference-Cited by-同舟云学术

MULTI-POLYLOGS AT TWELFTH ROOTS OF UNITY AND SPECIAL VALUES OF WITTEN MULTIPLE ZETA FUNCTION ATTACHED TO THE EXCEPTIONAL LIE ALGEBRA 𝔤2

Published:2010-04 Issue:02 Volume:09 Page:327-337
ISSN:0219-4988
Container-title:Journal of Algebra and Its Applications
language:en
Short-container-title:J. Algebra Appl.

Author:

ZHAO JIANQIANG¹²

Affiliation:

1. Department of Mathematics, Eckerd College, St. Petersburg, FL 33711, USA

2. Max-Planck Institut für Mathematik, Vivatsgasse 7, 53111 Bonn, Germany

Abstract

In this note, we shall study the Witten multiple zeta function associated with the exceptional Lie algebra 𝔤2. 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.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S021949881000394X

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