Reassessing Riemann's Paper On the Number of Primes Less Than a Given Magnitude
In this book, the author pays tribute to Bernhard Riemann (1826-1866), a mathematician with revolutionary ideas, whose work on the theory of integration, the Fourier transform, the hypergeometric differential equation, etc. contributed immensely to mathematical physics. The text concentrates in part...
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| Format: | eBook |
| Language: | English |
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Cham
Springer International Publishing
2021, 2021
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| Edition: | 2nd ed. 2021 |
| Series: | SpringerBriefs in History of Science and Technology
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| Subjects: | |
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| Collection: | Springer eBooks 2005- - Collection details see MPG.ReNa |
Table of Contents:
- Preface
- Towards Euler's Product Formula and Riemann’s Extension of the Zeta Function
- Prime Power Number Counting Function
- Riemann as an Expert in Fourier Transforms
- On the Way to Riemann’s Entire Function ζ(s)
- The Product Representation of ξ(s) and ζ(s) by Riemann (1859)
- Derivation of Von Mangoldt’s Formula for ψ(x)
- The Number of Roots in the Critical Strip
- Riemann’s Zeta Function Regularization
- ζ-Function Regularization of the Partition Function of the Harmonic Oscillator
- ζ-Function Regularization of the Partition Function of the Fermi Oscillator
- The Zeta-Function in Quantum Electrodynamics (QED)
- Summary of Euler-Riemann Formulae
- Appendix