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出版时间:2021-03

出版社:高等教育出版社

以下为《Riemann zeta函数讲义(影印版)》的配套数字资源,这些资源在您购买图书后将免费附送给您:
  • 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
目录

 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