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ALTERNATING EULER SUMS AND SPECIAL VALUES OF THE WITTEN MULTIPLE ZETA FUNCTION ATTACHED TO

Part of: Zeta and $L$-functions: analytic theory Lie algebras and Lie superalgebras

Published online by Cambridge University Press:  18 February 2011

JIANQIANG ZHAO
JIANQIANG ZHAO*
Affiliation:
Department of Mathematics, Eckerd College, St Petersburg FL 33711, USA (email: [email protected])
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Abstract

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We study the Witten multiple zeta function associated with the Lie algebra . Our main result shows that its special values at nonnegative integers are always expressible by alternating Euler sums. More precisely, every such special value of weight w at least 2 is a finite ℚ-linear combination of alternating Euler sums of weight w and depth at most 2, except when the only nonzero argument is one of the two last variables, in which case ζ(w−1) is needed.

Keywords

Witten zeta functionsWitten volume formulasalternating Euler sums

MSC classification

Secondary: 11M41: Other Dirichlet series and zeta functions 17B20: Simple, semisimple, reductive (super)algebras
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 89 , Issue 3 , December 2010 , pp. 419 - 430
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2011

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