| 书目名称 | Fractal Geometry, Complex Dimensions and Zeta Functions | | 副标题 | Geometry and Spectra | | 编辑 | Michel L. Lapidus,Machiel van 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 of this Second Edition:.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 dynamical zeta functions associated with a fractal.Examples of such explicit formulas include a Prime Orbit Theorem with error term for self-similar flows, and a geometric tube formula.The method of Diophantine approximation is used to study self-similar strings and flows .Analytical and geometric methodsare used to obtain new results about the vertical distribution of zeros of number-theoretic and other zeta functions.Throughout, new results are examined and a new definition of fractality as the presence of nonreal complex dimensions with positive real parts | | 出版日期 | Book 2013Latest edition | | 关键词 | Riemann hypothesis; cantor strings; complex dimensions; fractality; inverse spectral problems; minkowski | | 版次 | 2 | | doi | https://doi.org/10.1007/978-1-4614-2176-4 | | isbn_softcover | 978-1-4899-8838-6 | | isbn_ebook | 978-1-4614-2176-4Series ISSN 1439-7382 Series E-ISSN 2196-9922 | | issn_series | 1439-7382 | | copyright | Springer Science+Business Media New York 2013 |
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书目名称Fractal Geometry, Complex Dimensions and Zeta Functions影响因子(影响力)
书目名称Fractal Geometry, Complex Dimensions and Zeta Functions影响因子(影响力)学科排名
书目名称Fractal Geometry, Complex Dimensions and Zeta Functions网络公开度
书目名称Fractal Geometry, Complex Dimensions and Zeta Functions网络公开度学科排名
书目名称Fractal Geometry, Complex Dimensions and Zeta Functions被引频次
书目名称Fractal Geometry, Complex Dimensions and Zeta Functions被引频次学科排名
书目名称Fractal Geometry, Complex Dimensions and Zeta Functions年度引用
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书目名称Fractal Geometry, Complex Dimensions and Zeta Functions读者反馈
书目名称Fractal Geometry, Complex Dimensions and Zeta Functions读者反馈学科排名
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发表于 2025-3-21 18:33:09
