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Lectures on the Riemann zeta function /

Bibliographic Details
Main Author: Iwaniec, Henryk
Corporate Author: EBSCOhost
Format: eBook
Language:English
Published: Providence, Rhode Island : American Mathematical Society, [2014]
Series:University lecture series (Providence, R.I.) ; 62.
Subjects:
Riemann, Bernhard, > 1826-1866.
Functions, Zeta.
Riemann hypothesis.
Numbers, Prime.
Electronic books.
Online Access:Connect to the full text of this electronic book
Table of Contents:
  • Part 1. Classical Topics
  • 1. Panorama of Arithmetic Functions
  • 2. The Euler-Maclaurin Formula
  • 3. Tchebyshev's Prime Seeds
  • 4. Elementary Prime Number Theorem
  • 5. The Riemann Memoir
  • 6. The Analytic Continuation
  • 7. The Functional Equation
  • 8. The Product Formula over the Zeros
  • 9. The Asymptotic Formula for N(T)
  • 10. The Asymptotic Formula for?(x)
  • 11. The Zero-free Region and the PNT
  • 12. Approximate Functional Equations
  • 13. The Dirichlet Polynomials
  • 14. Zeros off the Critical Line
  • 15. Zeros on the Critical Line
  • Part 2. The Critical Zeros after Levinson
  • 16. Introduction
  • 17. Detecting Critical Zeros
  • 18. Conrey's Construction
  • 19. The Argument Variations
  • 20. Attaching a Mollifier
  • 21. The Littlewood Lemma
  • 22. The Principal Inequality
  • 23. Positive Proportion of the Critical Zeros
  • 24. The First Moment of Dirichlet Polynomials
  • 25. The Second Moment of Dirichlet Polynomials
  • 26. The Diagonal Terms
  • 27. The Off-diagonal Terms
  • 28. Conclusion
  • 29. Computations and the Optimal Mollifier
  • Appendix A. Smooth Bump Functions
  • Appendix B. The Gamma Function.