Reassessing Riemann's Paper On the Number of Primes Less Than a Given Magnitude /

• Main Author: Dittrich, Walter (Author, http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2018.
• Edition: 1st ed. 2018.
• Series: SpringerBriefs in History of Science and Technology,
• Subjects: Mathematics.; History.; Number theory.; Quantum field theory.; String theory.; History of Mathematical Sciences.; Number Theory.; Quantum Field Theories, String Theory.

In this book, the author pays tribute to Bernhard Riemann (1826-1866), mathematician with revolutionary ideas, whose work on the theory of integration, the Fourier transform, the hypergeometric differential equation, etc. contributed immensely to mathematical physics. This book concentrates in parti...

Table of Contents:

• Preface
• Introduction
• Short Biography of Bernhard Riemann (1826 - 1866)
• 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
• Supplements
• Appendix.