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Lectures on the Riemann zeta function / H. Iwaniec.

By: Iwaniec, Henryk.
Material type: materialTypeLabelBookSeries: University lecture series ; volume 62.Publisher: Providence, Rhode Island : American Mathematical Society, [2014]Copyright date: ©2014Description: vii, 119 pages : illustrations ; 26 cm.Content type: text Media type: unmediated Carrier type: volumeISBN: 9781470418519 (alk. paper); 1470418517 (alk. paper).Other title: Riemann zeta function.Subject(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 functionsOther classification: 11N05 (11N37)
Contents:
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] --
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Últimas adquisiciones 11 Iw96r (Browse shelf) Checked out Tapa rústica 2020-08-31 A-9297

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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