Zeta functions of groups and rings

Marcus du Sautoy, Luke Woodward (auth.)354074701X, 9783540747017, 9783540747765, 3540747761

Zeta functions have been a powerful tool in mathematics over the last two centuries. This book considers a new class of non-commutative zeta functions which encode the structure of the subgroup lattice in infinite groups. The book explores the analytic behaviour of these functions together with an investigation of functional equations. Many important examples of zeta functions are calculated and recorded providing an important data base of explicit examples and methods for calculation.

Table of contents :
Front Matter….Pages I-XII
Introduction….Pages 1-20
Nilpotent Groups: Explicit Examples….Pages 21-68
Soluble Lie Rings….Pages 69-82
Local Functional Equations….Pages 83-119
Natural Boundaries I: Theory….Pages 121-153
Natural Boundaries II: Algebraic Groups….Pages 155-167
Natural Boundaries III: Nilpotent Groups….Pages 169-177
Back Matter….Pages 179-212