| 书目名称 | Fractal Geometry, Complex Dimensions and Zeta Functions | | 副标题 | Geometry and Spectra | | 编辑 | Michel L. Lapidus,Machiel Frankenhuijsen | | 视频video | | | 概述 | The Riemann hypothesis is given a natural geometric reformulation in the context of vibrating fractal strings.Number theory, spectral geometry, and fractal geometry are interlinked in this in-depth st | | 丛书名称 | Springer Monographs in Mathematics | | 图书封面 |  | | 描述 | .Number theory, spectral geometry, and fractal geometry are interlinked in this in-depth study of the vibrations of fractal strings, that is, one-dimensional drums with fractal boundary...Key Features: ..- The Riemann hypothesis is given a natural geometric reformulation in the context of vibrating fractal strings..- Complex dimensions of a fractal string, defined as the poles of an associated zeta function, are studied in detail, then used to understand the oscillations intrinsic to the corresponding fractal geometries and frequency spectra..- Explicit formulas are extended to apply to the geometric, spectral, and dynamic zeta functions associated with a fractal..- Examples of such formulas include Prime Orbit Theorem with error term for self-similar flows, and a tube formula..- The method of diophantine approximation is used to study self-similar strings and flows..- Analytical and geometric methods are used to obtain new results about the vertical distribution of zeros of number-theoretic and other zeta functions..Throughout new results are examined. The final chapter gives a new definition of fractality as the presence of nonreal complex dimensions with positive real parts...Th | | 出版日期 | Book 20061st edition | | 关键词 | Diophantine approximation; Number theory; Prime; Riemann hypothesis; cantor strings; complex dimensions; i | | 版次 | 1 | | doi | https://doi.org/10.1007/978-0-387-35208-4 | | isbn_ebook | 978-0-387-35208-4Series ISSN 1439-7382 Series E-ISSN 2196-9922 | | issn_series | 1439-7382 | | copyright | Springer-Verlag New York 2006 |
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发表于 2025-3-21 17:43:05
