Multiplicative Number Theory I
Multiplicative Number Theory I
Robert C. Vaughan, Pennsylvania State University
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
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
Product details
July 2012Paperback
9781107405820
572 pages
229 × 152 × 32 mm
0.83kg
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.
