Lectures on the Riemann zeta function / H. Iwaniec.
Series University lecture series ; volume 62Editor: Providence, Rhode Island : American Mathematical Society, [2014]Fecha de copyright: ©2014Descripción: vii, 119 pages : illustrations ; 26 cmTipo de contenido: text Tipo de medio: unmediated Tipo de portador: volumeISBN: 9781470418519 (alk. paper); 1470418517 (alk. paper)Otro título: Riemann zeta functionTema(s): Riemann, Bernhard, 1826-1866 | Functions, Zeta | Riemann hypothesis | Numbers, Prime | Number theory -- Multiplicative number theory -- Distribution of primes | Number theory -- Multiplicative number theory -- Asymptotic results on arithmetic functionsOtra clasificación: 11N05 (11N37)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] Chapter 21. The Littlewood Lemma [77] Chapter 22. The Principal Inequality [79] Chapter 23. Positive Proportion of the Critical Zeros [81] Chapter 24. The First Moment of Dirichlet Polynomials [83] Chapter 25. The Second Moment of Dirichlet Polynomials [85] Chapter 26. The Diagonal Terms [87] Chapter 27. The Off-diagonal Terms [95] Chapter 28. Conclusion [103] Chapter 29. Computations and the Optimal Mollifier [107] Appendix A. Smooth Bump Functions [111] Appendix B. The Gamma Function [115] Bibliography [117] Index [119]
| Item type | Home library | Shelving location | Call number | Materials specified | Status | Notes | Date due | Barcode |
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Instituto de Matemática, CONICET-UNS | Últimas adquisiciones | 11 Iw96r (Browse shelf) | Checked out | Tapa rústica | 2024-02-05 | A-9297 |
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Incluye referencias bibliográficas (p. 117) e índice.
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] --
Chapter 21. The Littlewood Lemma [77] --
Chapter 22. The Principal Inequality [79] --
Chapter 23. Positive Proportion of the Critical Zeros [81] --
Chapter 24. The First Moment of Dirichlet Polynomials [83] --
Chapter 25. The Second Moment of Dirichlet Polynomials [85] --
Chapter 26. The Diagonal Terms [87] --
Chapter 27. The Off-diagonal Terms [95] --
Chapter 28. Conclusion [103] --
Chapter 29. Computations and the Optimal Mollifier [107] --
Appendix A. Smooth Bump Functions [111] --
Appendix B. The Gamma Function [115] --
Bibliography [117] --
Index [119] --
MR, MR3241276
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