Lecture Notes in Mathematics

Zeta Functions of Groups and Rings

Authors: du Sautoy, Marcus, Woodward, Luke

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About this book

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.

Reviews

From the reviews:

"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"The purpose of this stimulating book is to bring into print significant and as yet unpublished work from different areas of the theory of zeta functions of groups.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)


Table of contents (7 chapters)

Buy this book

eBook £31.99
price for United Kingdom (gross)
  • ISBN 978-3-540-74776-5
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover £40.99
price for United Kingdom (gross)
  • ISBN 978-3-540-74701-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Zeta Functions of Groups and Rings
Authors
Series Title
Lecture Notes in Mathematics
Series Volume
1925
Copyright
2008
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-540-74776-5
DOI
10.1007/978-3-540-74776-5
Softcover ISBN
978-3-540-74701-7
Series ISSN
0075-8434
Edition Number
1
Number of Pages
XII, 212
Topics