# Multiplicative Number Theory I. Classical Theory (Cambridge Studies in Advanced Mathematics)

Cambridge University Press

Edition: Reprint, 7/26/2012

EAN 9781107405820, ISBN10: 1107405823

Paperback, 572 pages, 22.9 x 15.2 x 3.6 cm

Language: English

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.

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.