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Multiplicative Number Theory I
Classical Theory

Part of Cambridge Studies in Advanced Mathematics

  • Date Published: July 2012
  • availability: Available
  • format: Paperback
  • isbn: 9781107405820

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  • Prime numbers are the multiplicative building blocks of natural numbers. Understanding their overall influence and especially their distribution gives rise to central questions in mathematics and physics. In particular their finer distribution is closely connected with the Riemann hypothesis, the most important unsolved problem in the mathematical world. Assuming only subjects covered in a standard degree in mathematics, the authors comprehensively cover all the topics met in first courses on multiplicative number theory and the distribution of prime numbers. They bring their extensive and distinguished research expertise to bear in preparing the student for intelligent reading of the more advanced research literature. This 2006 text, which is based on courses taught successfully over many years at Michigan, Imperial College and Pennsylvania State, is enriched by comprehensive historical notes and references as well as over 500 exercises.

    • Large collection of stimulating problems associated with each section
    • Extensive references to both historical background and further development of subject
    • Based extensively on the material used successfully at the University of Michigan, Imperial College London, and Penn State University
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    Reviews & endorsements

    'The text is very well written and accessible to students. On many occasions the authors explicitly describe basic methods known to everyone working in the field, but too often skipped in textbooks. This book may well become the standard introduction to analytic number theory.' Zentralblatt MATH

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    Product details

    • Date Published: July 2012
    • format: Paperback
    • isbn: 9781107405820
    • length: 572 pages
    • dimensions: 229 x 152 x 32 mm
    • weight: 0.83kg
    • availability: Available
  • Table of Contents

    Preface
    Notation
    1. Dirichlet series-I
    2. The elementary theory of arithmetic functions
    3. Principles and first examples of sieve methods
    4. Primes in arithmetic progressions-I
    5. Dirichlet series-II
    6. The prime number theorem
    7. Applications of the prime number theorem
    8. Further discussion of the prime number theorem
    9. Primitive characters and Gauss sums
    10. Analytic properties of the zeta function and L-functions
    11. Primes in arithmetic progressions-II
    12. Explicit formulae
    13. Conditional estimates
    14. Zeros
    15. Oscillations of error terms
    Appendix A. The Riemann-Stieltjes integral
    Appendix B. Bernoulli numbers and the Euler-MacLaurin summation formula
    Appendix C. The gamma function
    Appendix D. Topics in harmonic analysis.

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    Multiplicative Number Theory I

    Hugh L. Montgomery, Robert C. Vaughan

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  • Authors

    Hugh L. Montgomery, University of Michigan, Ann Arbor

    Robert C. Vaughan, Pennsylvania State University

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