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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Hlavní autor: Dittrich, Walter (Autor)
Médium: Elektronický zdroj E-kniha
Jazyk:angličtina
Vydáno: Cham : Springer International Publishing, 2018.
Vydání:1st ed. 2018.
Edice:SpringerBriefs in History of Science and Technology,
Témata:
Mathematics.
History.
Number theory.
Quantum field theory.
String theory.
ISBN:9783319914824
ISSN:2211-4564
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Obsah:
  • 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.

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