# Lectures on the Riemann Zeta Function

### About this Title

**H. Iwaniec**, *Rutgers University, Piscataway, NJ*

Publication: University Lecture Series

Publication Year
2014: Volume 62

ISBNs: 978-1-4704-1851-9 (print); 978-1-4704-1891-5 (online)

DOI: http://dx.doi.org/10.1090/ulect/062

MathSciNet review: MR3241276

MSC: Primary 11N05; Secondary 11N37

### Table of Contents

**Front/Back Matter**

**Part 1. Classical topics **

- Chapter 1. Panorama of arithmetic functions
- Chapter 2. The Euler–Maclaurin formula
- Chapter 3. Tchebyshev’s prime seeds
- Chapter 4. Elementary prime number theorem
- Chapter 5. The Riemann memoir
- Chapter 6. The analytic continuation
- Chapter 7. The functional equation
- Chapter 8. The product formula over the zeros
- Chapter 9. The asymptotic formula for $N(T)$
- Chapter 10. The asymptotic formula for $\psi (x)$
- Chapter 11. The zero-free region and the PNT
- Chapter 12. Approximate functional equations
- Chapter 13. The Dirichlet polynomials
- Chapter 14. Zeros off the critical line
- Chapter 15. Zeros on the critical line

**Part 2. The critical zeros after Levinson **

- Chapter 16. Introduction
- Chapter 17. Detecting critical zeros
- Chapter 18. Conrey’s construction
- Chapter 19. The argument variations
- Chapter 20. Attaching a mollifier
- Chapter 21. The Littlewood lemma
- Chapter 22. The principal inequality
- Chapter 23. Positive proportion of the critical zeros
- Chapter 24. The first moment of Dirichlet polynomials
- Chapter 25. The second moment of Dirichlet polynomials
- Chapter 26. The diagonal terms
- Chapter 27. The off-diagonal terms
- Chapter 28. Conclusion
- Chapter 29. Computations and the optimal mollifier
- Appendix A. Smooth bump functions
- Appendix B. The gamma function