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.
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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