Multiplicative Number Theory I

Produktbeschreibung

A 2006 text based on courses taught successfully over many years at Michigan, Imperial College and Pennsylvania State. 

Inhaltsverzeichnis

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.