The theory of zeta-functions of root systems

The theory of zeta-functions of root systems / Yasushi Komori, Kohji Matsumoto, Hirofumi Tsumura.

The contents of this book was created by the authors as a simultaneous generalization of Witten zeta-functions, MordellTornheim multiple zeta-functions, and EulerZagier multiple zeta-functions. Zeta-functions of root systems are defined by certain multiple series, given in terms of root systems. The...

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Bibliographic Details
Main Author: Komori, Yasushi
Other Authors: Matsumoto, Kohji, Tsumura, Hirofumi
Format: eBook
Language:English
Published: Singapore : Springer, 2023.
Series:Springer monographs in mathematics.
Subjects:
Functions, Zeta.
Online Access:Click for online access
Table of Contents:
  • Introduction
  • Fundamentals of the theory of Lie algebras and root systems
  • Definitions and examples
  • Values at positive even integer points
  • Convex polytopes and the rationality
  • The recursive structure
  • The meromorphic continuation
  • Functional relations (I)
  • Functional relations (II)
  • Poincare polynomials and values at integer points
  • The case of the exceptional algebra G2
  • Applications to multiple zeta values (I)
  • Applications to multiple zeta values (II)
  • L-functions
  • Zeta-functions of Lie groups
  • Lattice sums of hyperplane arrangements
  • Miscellaneous results.

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