Hugh L. Montgomery (Ann Arbor University of Michigan), Robert C. Vaughan (Pennsylvania State University)

Multiplicative Number Theory I. Classical Theory

• Gebundenes Buch

Produktbeschreibung

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.

Produktdetails

• Cambridge Studies in Advanced Mathematics
• Verlag: Cambridge University Press
• Seitenzahl: 572
• Erscheinungstermin: 19. Mai 2011
• Englisch
• Abmessung: 235mm x 157mm x 38mm
• Gewicht: 1004g
• ISBN-13: 9780521849036
• ISBN-10: 0521849039
• Artikelnr.: 21254024

Autorenporträt

Hugh Montgomery is a Professor of Mathematics at the University of Michigan.
Robert Vaughan is a Professor of Mathematics at Pennsylvannia State University.

Inhaltsangabe

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.