Progress in Mathematics

Non-vanishing of L-Functions and Applications

Authors: Murty, Ram M., Murty, Kumar V.

Free Preview

Buy this book

eBook $79.99
price for USA in USD
  • ISBN 978-3-0348-8956-8
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $99.99
price for USA in USD
  • ISBN 978-3-0348-9843-0
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
About this book

This monograph brings together a collection of results on the non-vanishing of L­ functions. The presentation, though based largely on the original papers, is suitable for independent study. A number of exercises have also been provided to aid in this endeavour. The exercises are of varying difficulty and those which require more effort have been marked with an asterisk. The authors would like to thank the Institut d'Estudis Catalans for their encouragement of this work through the Ferran Sunyer i Balaguer Prize. We would also like to thank the Institute for Advanced Study, Princeton for the excellent conditions which made this work possible, as well as NSERC, NSF and FCAR for funding. Princeton M. Ram Murty August, 1996 V. Kumar Murty Introduction Since the time of Dirichlet and Riemann, the analytic properties of L-functions have been used to establish theorems of a purely arithmetic nature. The distri­ bution of prime numbers in arithmetic progressions is intimately connected with non-vanishing properties of various L-functions. With the subsequent advent of the Tauberian theory as developed by Wiener and Ikehara, these arithmetical the­ orems have been shown to be equivalent to the non-vanishing of these L-functions on the line Re(s) = 1. In the 1950's, a new theme was introduced by Birch and Swinnerton-Dyer.

Reviews

From the book reviews:

“This is the softcover reprint of a monograph that was awarded the Ferran Sunyer i Balaguer prize in 1996. It is devoted to a recurring theme in number theory, namely that the non-vanishing of L-functions implies important arithmetical results. … Giving a well-informed overview of related results it will continue to be an important source of information for graduate students and researchers … .” (Ch. Baxa, Monatshefte für Mathematik, Vol. 173, 2014)

Table of contents (9 chapters)

Table of contents (9 chapters)

Buy this book

eBook $79.99
price for USA in USD
  • ISBN 978-3-0348-8956-8
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $99.99
price for USA in USD
  • ISBN 978-3-0348-9843-0
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
Loading...

Recommended for you

Loading...

Bibliographic Information

Bibliographic Information
Book Title
Non-vanishing of L-Functions and Applications
Authors
Series Title
Progress in Mathematics
Series Volume
157
Copyright
1997
Publisher
Birkhäuser Basel
Copyright Holder
Springer Basel AG
eBook ISBN
978-3-0348-8956-8
DOI
10.1007/978-3-0348-8956-8
Softcover ISBN
978-3-0348-9843-0
Series ISSN
0743-1643
Edition Number
1
Number of Pages
XI, 196
Number of Illustrations
2 b/w illustrations
Topics