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
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