Reassessing Riemann's Paper: On the Number of Primes Less Than a Given Magnitude free ebook download.

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Reassessing Riemann's Paper: On the Number of Primes Less Than a Given Magnitude free ebook download

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Mathematics

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Author(s):	Walter Dittrich

Date:	2020-11-24	Format:	pdf	Language:	English	ISBN/ASIN:	3030610489
Pages:		OCR:		Quality:		ISBN13:
Uploader:	maveriks	Upload Date:	1/5/2021 12:09:33 PM

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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 Riemanns 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 Riemanns 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 Riemanns 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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