© 1997

Non-vanishing of L-Functions and Applications


Part of the Progress in Mathematics book series (PM, volume 157)

Table of contents

  1. Front Matter
    Pages i-xi
  2. M. Ram Murty, V. Kumar Murty
    Pages 1-3
  3. M. Ram Murty, V. Kumar Murty
    Pages 5-23
  4. M. Ram Murty, V. Kumar Murty
    Pages 25-64
  5. M. Ram Murty, V. Kumar Murty
    Pages 65-73
  6. M. Ram Murty, V. Kumar Murty
    Pages 75-92
  7. M. Ram Murty, V. Kumar Murty
    Pages 93-132
  8. M. Ram Murty, V. Kumar Murty
    Pages 133-176
  9. M. Ram Murty, V. Kumar Murty
    Pages 177-185
  10. M. Ram Murty, V. Kumar Murty
    Pages 187-191
  11. Back Matter
    Pages 192-196

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.


Number theory alegbraic geometry arithmetic number theory prime number

Authors and affiliations

  1. 1.Department of MathematicsQueen’s UniversityKingstonCanada
  2. 2.Department of MathematicsUniversity of TorontoTorontoCanada

Bibliographic information

  • Book Title Non-vanishing of L-Functions and Applications
  • Authors Ram M. Murty
    Kumar V. Murty
  • Series Title Progress in Mathematics
  • Series Abbreviated Title Progress in Mathematics(Birkhäuser)
  • DOI
  • Copyright Information Springer Basel AG 1997
  • Publisher Name Birkhäuser, Basel
  • eBook Packages Springer Book Archive
  • Hardcover ISBN 978-3-7643-5801-3
  • Softcover ISBN 978-3-0348-9843-0
  • eBook ISBN 978-3-0348-8956-8
  • Series ISSN 0743-1643
  • Series E-ISSN 2296-505X
  • Edition Number 1
  • Number of Pages XI, 196
  • Number of Illustrations 2 b/w illustrations, 0 illustrations in colour
  • Topics Algebraic Geometry
  • Buy this book on publisher's site


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)