Contents Preface vii Part 1. Classical Topics 1 Chapter 1. Panorama of Arithmetic Functions 3 Chapter 2. The Euler–Maclaurin Formula 9 Chapter 3. Tchebyshev’s Prime Seeds 13 Chapter 4. Elementary Prime Number Theorem 15 Chapter 5. The Riemann Memoir 21 Chapter 6. The Analytic Continuation 23 Chapter 7. The Functional Equation 25 Chapter 8. The Product Formula over the Zeros 27 Chapter 9. The Asymptotic Formula for N(T ) 33 Chapter 10. The Asymptotic Formula for ψ(x) 37 Chapter 11. The Zero-free Region and the PNT 41 Chapter 12. Approximate Functional Equations 43 Chapter 13. The Dirichlet Polynomials 47 Chapter 14. Zeros off the Critical Line 55 Chapter 15. Zeros on the Critical Line 57 Part 2. The Critical Zeros after Levinson 63 Chapter 16. Introduction 65 Chapter 17. Detecting Critical Zeros 67 Chapter 18. Conrey’s Construction 69 Chapter 19. The Argument Variations 71 Chapter 20. Attaching a Mollifier 75 v
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