| 书目名称 | Reassessing Riemann‘s Paper |
| 副标题 | On the Number of Pri |
| 编辑 | Walter Dittrich |
| 视频video | |
| 概述 | Didactically improved presentation of selected applications of Riemann’s ?-function.Provides three new chapters and a summary of Euler-Riemann formulae.Emphasizes the importance of Riemann’s functiona |
| 丛书名称 | SpringerBriefs in History of Science and Technology |
| 图书封面 |  |
| 描述 | .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.. . |
| 出版日期 | Book 2021Latest edition |
| 关键词 | Riemann‘s Paper on Prime Numbers; Zeta-function regularization; Functional equation; Fourier transform; |
| 版次 | 2 |
| doi | https://doi.org/10.1007/978-3-030-61049-4 |
| isbn_softcover | 978-3-030-61048-7 |
| isbn_ebook | 978-3-030-61049-4Series ISSN 2211-4564 Series E-ISSN 2211-4572 |
| issn_series | 2211-4564 |
| copyright | The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 |
发表于 2025-3-21 18:56:49
