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), 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...

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Bibliographic Details
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:
Online Access:Full Text via HEAL-Link
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.