On Witten Multiple Zeta-Functions Associated with Semisimple Lie Algebras III

2009/07/06 by Yasushi Komori, Kohji Matsumoto, Hirofumi Tsumura · 3 citations
Chemistry · Mathematics · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Algebra over a field #Bernoulli number #Bernoulli's principle #Geometry #Mathematics #Molecular spectroscopy and chirality #Physics #Pure mathematics #Root (linguistics) #Symmetry (geometry) #math.NT #msc:11M41 #msc:17B20 #msc:40B05

paper · pdf · doi:10.1007/978-0-8176-8334-4_11

published as Progress in Math. 300, Birkhauser, 2012, pp. 223-286 · 49 pages

arxiv created 2009/07/06 · openalex publication_date 2012/01/01 · arxiv updated 2016/04/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We prove certain general forms of functional relations among Witten multiple zeta-functions in several variables (or zeta-functions of root systems). The structural background of these functional relations is given by the symmetry with respect to Weyl groups. From these relations, we can deduce explicit expressions of values of Witten zeta-functions at positive even integers, which are written in terms of generalized Bernoulli numbers of root systems. Furthermore, we introduce generating functions of Bernoulli numbers of root systems, using which we can give an algorithm of calculating Bernoulli numbers of root systems.

Citations

• Decompositions of Rational Convex Polytopes
• Introduction to Analytic Number Theory

Cited by

• On Witten multiple zeta-functions associated with semisimple Lie algebras II
• Shuffle products for multiple zeta values and partial fraction decompositions of zeta-functions of root systems
• A study on multiple zeta values from the viewpoint of zeta-functions of root systems