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© 1980

Multiplicative Number Theory

Textbook

Part of the Graduate Texts in Mathematics book series (GTM, volume 74)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Harold Davenport
    Pages 1-11
  3. Harold Davenport
    Pages 12-16
  4. Harold Davenport
    Pages 17-26
  5. Harold Davenport
    Pages 35-42
  6. Harold Davenport
    Pages 43-53
  7. Harold Davenport
    Pages 54-58
  8. Harold Davenport
    Pages 59-64
  9. Harold Davenport
    Pages 65-72
  10. Harold Davenport
    Pages 73-73
  11. Harold Davenport
    Pages 74-78
  12. Harold Davenport
    Pages 79-83
  13. Harold Davenport
    Pages 84-87
  14. Harold Davenport
    Pages 88-96
  15. Harold Davenport
    Pages 97-100
  16. Harold Davenport
    Pages 101-103
  17. Harold Davenport
    Pages 104-110
  18. Harold Davenport
    Pages 111-114
  19. Harold Davenport
    Pages 115-120

About this book

Introduction

Although it was in print for a short time only, the original edition of Multiplicative Number Theory had a major impact on research and on young mathematicians. By giving a connected account of the large sieve and Bombieri's theorem, Professor Davenport made accessible an important body of new discoveries. With this stimula­ tion, such great progress was made that our current understanding of these topics extends well beyond what was known in 1966. As the main results can now be proved much more easily. I made the radical decision to rewrite §§23-29 completely for the second edition. In making these alterations I have tried to preserve the tone and spirit of the original. Rather than derive Bombieri's theorem from a zero density estimate tor L timctions, as Davenport did, I have chosen to present Vaughan'S elementary proof of Bombieri's theorem. This approach depends on Vaughan's simplified version of Vinogradov's method for estimating sums over prime numbers (see §24). Vinogradov devised his method in order to estimate the sum LPH e(prx); to maintain the historical perspective I have inserted (in §§25, 26) a discussion of this exponential sum and its application to sums of primes, before turning to the large sieve and Bombieri's theorem. Before Professor Davenport's untimely death in 1969, several mathematicians had suggested small improvements which might be made in Multiplicative Number Theory, should it ever be reprinted.

Keywords

Microsoft Access Multiplikative Zahlentheorie Prime Sieve arithmetic boundary element method number theory prime number proof theorem time

Authors and affiliations

  1. 1.Cambridge UniversityCambridgeEngland

Bibliographic information

  • Book Title Multiplicative Number Theory
  • Authors H. Davenport
  • Series Title Graduate Texts in Mathematics
  • DOI https://doi.org/10.1007/978-1-4757-5927-3
  • Copyright Information Springer-Verlag New York 1980
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Hardcover ISBN 978-0-387-90533-4
  • Softcover ISBN 978-1-4757-5929-7
  • eBook ISBN 978-1-4757-5927-3
  • Series ISSN 0072-5285
  • Edition Number 2
  • Number of Pages XIII, 177
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Additional Information Originally published by Markham Publishing Co., 1967
  • Topics Number Theory
  • Buy this book on publisher's site

Reviews

From the reviews of the third edition:

"The book under review is one of the most important references in the multiplicative number theory, as its title mentions exactly. … Davenport’s book covers most of the important topics in the theory of distribution of primes and leads the reader to serious research topics … . is very well written. … is useful for graduate students, researchers and for professors. It is a very good text source specially for graduate levels, but even is fruitful for undergraduates." (Mehdi Hassani, MathDL, July, 2008)