Riemann zeta函数讲义(影印版)
作者: H.Iwaniec
出版时间:2021-03
出版社:高等教育出版社
- 高等教育出版社
- 9787040556308
- 1版
- 369849
- 46253882-8
- 精装
- 16开
- 2021-03
- 210
- 136
- 理学
- 数学
- 数学类
- 研究生及以上
前辅文
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 ψ(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
Bibliography
Index