Multiplicative Number Theory I. Classical Theory

Informationen zum Autor Hugh Montgomery is a Professor of Mathematics at the University of Michigan. Robert Vaughan is a Professor of Mathematics at Pennsylvannia State University. Klappentext A 2006 text based on courses taught successfully over many years at Michigan, Imperial College and Pennsylvania State. Zusammenfassung 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 this 2006 text! the authors bring their extensive and distinguished research expertise to prepare the student for intelligent reading of the more advanced research literature. 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.

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

Zusammenfassung
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 this 2006 text, the authors bring their extensive and distinguished research expertise to prepare the student for intelligent reading of the more advanced research literature.

Inhalt
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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