Zeta Functions of Groups and Rings / Edition 1

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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. It explores the analytic behavior of these functions together with an investigation of functional equations. The book examines many important examples of zeta functions, providing an important database of explicit examples and methods for calculation.

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Editorial Reviews

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"The book starts with a short lovely description of several classical zeta function … . It also contains a large number of examples of groups for which these zeta functions were explicitly computed. … it certainly will be a basic text for anyone who plans to work in this area. … These surely will be valuable for inspiring further developments." (Alexander Lubotzky, Mathematical Reviews, Issue 2009 d)

"The purpose of this stimulating book is to bring into print significant and as yet unpublished work from different areas of the theory of zeta functions of groups. … The book will be not only a valuable reference for people working in this area, but also a fascinating reading for everybody who wants to understand the role zeta functions have in group theory and the connections between subgroup growth and algebraic geometry over finite fields revealed by this theory." (Andrea Lucchini, Zentralblatt MATH, Vol. 1151, 2009)

“The authors have compiled a large body of facts and conjectures which will no doubt be most valuable for everyone working in this fascinating and very active field of research.” (C. Baxa, Monatshefte für Mathematik, Vol. 160 (3), June, 2010)

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Product Details

  • ISBN-13: 9783540747017
  • Publisher: Springer Berlin Heidelberg
  • Publication date: 12/14/2007
  • Series: Lecture Notes in Mathematics Series, #1925
  • Edition description: 2008
  • Edition number: 1
  • Pages: 212
  • Product dimensions: 9.21 (w) x 6.14 (h) x 0.48 (d)

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.

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