Reassessing Riemann's paper on the number of primes less than a given magnitude / [electronic resource] :

• 作者： Dittrich, Walter.
• 其他作者：
  • SpringerLink (Online service)
• 其他題名：
  • SpringerBriefs in history of science and technology.
• 出版： Cham : Springer International Publishing :Imprint: Springer
• 版本：Second edition.
• 叢書名： SpringerBriefs in history of science and technology,
• 主題： Riemann hypothesis. , History of Mathematical Sciences. , Number Theory. , Elementary Particles, Quantum Field Theory.
• ISBN： 9783030610494 (electronic bk.) 、 9783030610487 (paper)
• FIND@SFXID: CGU
• 資料類型: 電子書
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• 摘要註: 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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