Zeta Functions of Groups and Rings

• Main Authors: Sautoy, Marcus du (Author), Woodward, Luke (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg, 2008.
• Series: Lecture Notes in Mathematics, 1925
• Subjects: Mathematics.; Group theory.; Nonassociative rings.; Rings (Algebra).; Number theory.; Group Theory and Generalizations.; Number Theory.; Non-associative Rings and Algebras.

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 i...

Table of Contents:

• Nilpotent Groups: Explicit Examples
• Soluble Lie Rings
• Local Functional Equations
• Natural Boundaries I: Theory
• Natural Boundaries II: Algebraic Groups
• Natural Boundaries III: Nilpotent Groups.