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

Author:

ZHAO JIANQIANG

Abstract

AbstractWe study the Witten multiple zeta function associated with the Lie algebra $\so $. 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.

Publisher

Cambridge University Press (CUP)

Subject

General Mathematics

Reference24 articles.

1. FUNCTIONAL RELATIONS FOR ZETA-FUNCTIONS OF ROOT SYSTEMS

2. [1] Borwein J. , Lisonek P. and Irvine P. , ‘An interface for evaluation of Euler sums’, available online at http://oldweb.cecm.sfu.ca/cgi-bin/EZFace/zetaform.cgi.

3. Standard relations of multiple polylogarithm values at roots of unity;Zhao;Doc. Math.,2010

4. [5] Komori Y. , Matsumoto K. and Tsumura H. , ‘On Witten multiple zeta-functions associated with semisimple Lie algebras III’, Proc. Conf. on Multiple Dirichlet Series and Applications to Automorphic Forms, Edinburgh, 2008, to appear. Preprint, arxiv: 0907.0955.

5. Derivation and double shuffle relations for multiple zeta values

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