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  3. Talteori

Reassessing Riemann's Paper

- On the Number of Primes Less Than a Given Magnitude
Af: Walter Dittrich Engelsk Paperback

Reassessing Riemann's Paper

- On the Number of Primes Less Than a Given Magnitude
Af: Walter Dittrich Engelsk Paperback
Tjek vores konkurrenters priser

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.


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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.


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Se mere i:
Produktdetaljer
Sprog: Engelsk
Sider: 107
ISBN-13: 9783030610487
Indbinding: Paperback
Udgave:
ISBN-10: 3030610489
Kategori: Talteori
Udg. Dato: 5 jan 2021
Længde: 0mm
Bredde: 155mm
Højde: 235mm
Forlag: Springer Nature Switzerland AG
Oplagsdato: 5 jan 2021
Forfatter(e): Walter Dittrich
Forfatter(e) Walter Dittrich

Kategori Talteori

ISBN-13 9783030610487

Sprog Engelsk

Indbinding Paperback

Sider 107

Udgave

Længde 0mm

Bredde 155mm

Højde 235mm

Udg. Dato 5 jan 2021

Oplagsdato 5 jan 2021

Forlag Springer Nature Switzerland AG

Kategori sammenhænge