SpringerBriefs in History of Science and Technology

Reassessing Riemann's Paper

On the Number of Primes Less Than a Given Magnitude

Authors: Dittrich, Walter

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  • Didactically improved presentation of selected applications of Riemann’s ζ-function
  • Provides three new chapters and a summary of Euler-Riemann formulae
  • Emphasizes the importance of Riemann’s functional equation for mathematics and physics  
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  • ISBN 978-3-030-61049-4
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Softcover $59.99
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About this book

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 particular on Riemann’s only work on prime numbers, including ideas – new at the time – such as analytical continuation into 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.

This revised and enhanced new edition contains three new chapters, two on the application of Riemann’s zeta-function regularization to obtain the partition function of a Bose (Fermi) oscillator and one on the zeta-function regularization in quantum electrodynamics. Appendix A2 has been re-written to make the calculations more transparent. A summary of Euler-Riemann formulae completes the book.


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 (11 chapters)

Table of contents (11 chapters)

Buy this book

eBook $44.99
price for USA in USD
  • ISBN 978-3-030-61049-4
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $59.99
price for USA in USD
  • ISBN 978-3-030-61048-7
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
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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
2021
Publisher
Springer International Publishing
Copyright Holder
The Author(s), under exclusive license to Springer Nature Switzerland AG
eBook ISBN
978-3-030-61049-4
DOI
10.1007/978-3-030-61049-4
Softcover ISBN
978-3-030-61048-7
Series ISSN
2211-4564
Edition Number
2
Number of Pages
XI, 107
Number of Illustrations
8 b/w illustrations, 10 illustrations in colour
Topics