Shop the Archives and get your next eBook for just 14.99! Stock up today >>

SpringerBriefs in History of Science and Technology

Reassessing Riemann's Paper

On the Number of Primes Less Than a Given Magnitude

Authors: Dittrich, Walter

  • Includes detailed explanation of the importance of Riemann’s zeta function
  • Provides explicit calculations leading to the derivation of Riemann’s relation between prime numbers and zeros of Riemann’s function
  • Emphasizes the importance of Riemann’s functional equation for mathematics and physics  
see more benefits

Buy this book

eBook 44,02 €
price for Spain (gross)
  • ISBN 978-3-319-91482-4
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover 57,19 €
price for Spain (gross)
  • ISBN 978-3-319-91481-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
About this book

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 particular on Riemann’s only work on prime numbers, including such then new ideas as analytical continuation in the complex plane and the product formula for entire functions. A detailed analysis of the zeros of the Riemann zeta function is presented. The impact of Riemann’s ideas on regularizing infinite values in field theory is also emphasized.

About the authors

Prof. Dr. Walter Dittrich was head of the quantum electrodynamics group at the University of Tübingen before his retirement in 2001 and is still actively publishing papers and books in classical and quantum physics. He received his doctorate under Prof. Heinz Mitter at Heisenberg’s institute in Munich and continued pre- and postdoc work at Brown University, Harvard and MIT. He profited immensely from lectures by and discussions with Profs. Herb Fried, Ken Johnson, Steve Weinberg, Julian Schwinger and, later on, at the Institute for Advanced Study (IAS) in Princeton, Steve Adler and David Gross at Princeton University. He started his work on gauge theories and QED in collaboration with Schwinger in the late 1960s. He was visiting professor at UCLA, Berkeley, Stanford and the IAS. He has over 30 years of teaching experience and is one of the key scientists in developing the theoretical framework of quantum electrodynamics.

Table of contents (8 chapters)

  • Towards Euler’s Product Formula and Riemann’s Extension of the Zeta Function

    Dittrich, Walter

    Pages 1-6

    Preview Buy Chapter 30,19 €
  • Prime Number Counting Function

    Dittrich, Walter

    Pages 7-12

    Preview Buy Chapter 30,19 €
  • Riemann as an Expert in Fourier Transforms

    Dittrich, Walter

    Pages 13-16

    Preview Buy Chapter 30,19 €
  • On the Way to Riemann’s Entire Function $$\xi (s)$$ ξ ( s )

    Dittrich, Walter

    Pages 17-23

    Preview Buy Chapter 30,19 €
  • The Product Representation of $$\xi (s)$$ ξ ( s ) and $$\zeta (s)$$ ζ ( s ) by Riemann (1859) and Hadamard (1893)

    Dittrich, Walter

    Pages 25-27

    Preview Buy Chapter 30,19 €

Buy this book

eBook 44,02 €
price for Spain (gross)
  • ISBN 978-3-319-91482-4
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover 57,19 €
price for Spain (gross)
  • ISBN 978-3-319-91481-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
Loading...

Recommended for you

Loading...

Bibliographic Information

Bibliographic Information
Book Title
Reassessing Riemann's Paper
Book Subtitle
On the Number of Primes Less Than a Given Magnitude
Authors
Series Title
SpringerBriefs in History of Science and Technology
Copyright
2018
Publisher
Springer International Publishing
Copyright Holder
The Author(s)
eBook ISBN
978-3-319-91482-4
DOI
10.1007/978-3-319-91482-4
Softcover ISBN
978-3-319-91481-7
Series ISSN
2211-4564
Edition Number
1
Number of Pages
XIX, 65
Number of Illustrations and Tables
4 b/w illustrations
Topics