Reassessing Riemann's paper : on the number of primes less than a given magnitude / Walter Dittrich.
2021
QA246
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Details
Title
Reassessing Riemann's paper : on the number of primes less than a given magnitude / Walter Dittrich.
Author
Dittrich, Walter.
Edition
2nd ed.
ISBN
9783030610494 (electronic bk.)
3030610497 (electronic bk.)
3030610489
9783030610487
3030610497 (electronic bk.)
3030610489
9783030610487
Publication Details
Cham : Springer, 2021.
Language
English
Description
1 online resource
Item Number
10.1007/978-3-030-61049-4 doi
Call Number
QA246
Dewey Decimal Classification
510.9
Summary
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.
Bibliography, etc. Note
Includes bibliographical references.
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Access limited to authorized users.
Digital File Characteristics
PDF
text file
text file
Source of Description
Online resource; title from PDF title page (SpringerLink, viewed March 8, 2021).
Series
SpringerBriefs in history of science and technology, 2211-4564
Available in Other Form
Reassessing Riemann's paper.
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