Multiplicative Number Theory I

Frontmatter

Contents

Preface

List of notations

1. Dirichlet Series I

2. The elementary theory of arithmetical 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 progression 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

Name Index

Subject Index