دانلود کتاب Reassessing Riemann's Paper: On the Number of Primes Less Than a Given Magnitude (SpringerBriefs in History of Science and Technology)

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Preface to the Second Edition
Preface to the First Edition
Contents
1 Towards Euler\'s Product Formula and Riemann\'s Extension of the Zeta Function
2 Prime Number Counting Function
3 Riemann as an Expert in Fourier Transforms
4 On the Way to Riemann\'s Entire Function ξ(s)
5 The Product Representation of ξ(s) and ζ(s) by Riemann (1859) and Hadamard (1893)
6 Derivation of von Mangoldt\'s Formula for Ψ(x)
7 The Number of Roots in the Critical Strip
8 Riemann\'s Zeta Function Regularization
9 ζ-Function Regularization of the Partition Function of the Harmonic Oscillator
10 ζ-Function Regularization of the Partition Function of the Fermi Oscillator
11 The Zeta Function in Quantum Electrodynamics (QED)
Summary of Euler-Riemann Formulae
Appendix A Supplements and Appendix
A.1 Supplements
A.1.1 The Origins of the Functional Equation for Dirichlet\'s Function
A.1.2 Riemann\'s Functional Equation
A.1.3 What Is a Function?
A.2 Appendix
A.2.1 Remarks on the Oscillatory Behavior of the Prime Counting Function
Acknowledgements
References