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Reassessing Riemann's paper = on the...

Dittrich, Walter.

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Reassessing Riemann's paper = on the number of primes less than a given magnitude /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Reassessing Riemann's paper/ by Walter Dittrich.
Reminder of title:	on the number of primes less than a given magnitude /
Author:	Dittrich, Walter.
Published:	Cham :Springer International Publishing : : 2021.,
Description:	xi, 107 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Riemann hypothesis. -
Online resource:	https://doi.org/10.1007/978-3-030-61049-4
ISBN:	9783030610494

Reassessing Riemann's paper = on the number of primes less than a given magnitude /
Dittrich, Walter.

Reassessing Riemann's paperon the number of primes less than a given magnitude /[electronic resource] :by Walter Dittrich. - Second edition. - Cham :Springer International Publishing :2021. - xi, 107 p. :ill., digital ;24 cm. - SpringerBriefs in history of science and technology,2211-4564. - SpringerBriefs in history of science and technology..

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.

ISBN: 9783030610494

Standard No.: 10.1007/978-3-030-61049-4doiSubjects--Topical Terms:

3259151
Riemann hypothesis.

LC Class. No.: QA246 / .D588 2021

Dewey Class. No.: 510.9

Reassessing Riemann's paper = on the number of primes less than a given magnitude /
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245 1 0 $a Reassessing Riemann's paper $h [electronic resource] : $b on the number of primes less than a given magnitude / $c by Walter Dittrich.
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300 $a xi, 107 p. : $b ill., digital ; $c 24 cm.
490 1 $a SpringerBriefs in history of science and technology, $x 2211-4564
520 $a 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.
650 0 $a Riemann hypothesis. $3 3259151
650 1 4 $a History of Mathematical Sciences. $3 1530523
650 2 4 $a Number Theory. $3 891078
650 2 4 $a Elementary Particles, Quantum Field Theory. $3 894026
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