| 书目名称 | Explorations in Complex Functions | | 编辑 | Richard Beals,Roderick S. C. Wong | | 视频video | | | 概述 | Illustrates a unique, accessible range of topics relevant across analysis and number theory.Includes pathways toward applications of the Schwarzian, the Riemann hypothesis, and parametrization of Riem | | 丛书名称 | Graduate Texts in Mathematics | | 图书封面 |  | | 描述 | .This textbook explores a selection of topics in complex analysis. From core material in the mainstream of complex analysis itself, to tools that are widely used in other areas of mathematics, this versatile compilation offers a selection of many different paths. Readers interested in complex analysis will appreciate the unique combination of topics and connections collected in this book.. . Beginning with a review of the main tools of complex analysis, harmonic analysis, and functional analysis, the authors go on to present multiple different, self-contained avenues to proceed. Chapters on linear fractional transformations, harmonic functions, and elliptic functions offer pathways to hyperbolic geometry, automorphic functions, and an intuitive introduction to the Schwarzian derivative. The gamma, beta, and zeta functions lead into .L.-functions, while a chapter on entire functions opens pathways to the Riemann hypothesis and Nevanlinna theory. Cauchy transforms give riseto Hilbert and Fourier transforms, with an emphasis on the connection to complex analysis. Valuable additional topics include Riemann surfaces, steepest descent, tauberian theorems, and the Wiener–Hopf method...Sho | | 出版日期 | Textbook 2020 | | 关键词 | Complex analysis textbook; Complex analysis for number theory; Linear fractional transformations; Harmo | | 版次 | 1 | | doi | https://doi.org/10.1007/978-3-030-54533-8 | | isbn_softcover | 978-3-030-54535-2 | | isbn_ebook | 978-3-030-54533-8Series ISSN 0072-5285 Series E-ISSN 2197-5612 | | issn_series | 0072-5285 | | copyright | Springer Nature Switzerland AG 2020 |
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发表于 2025-3-21 18:39:19
