| 書目名稱 | Fractal Geometry, Complex Dimensions and Zeta Functions | | 副標題 | Geometry and Spectra | | 編輯 | Michel L. Lapidus,Machiel van Frankenhuijsen | | 視頻video | http://file.papertrans.cn/348/347329/347329.mp4 | | 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 | | 叢書名稱 | Springer Monographs in Mathematics | | 圖書封面 |  | | 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 | | 關(guān)鍵詞 | 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 |
The information of publication is updating
書目名稱Fractal Geometry, Complex Dimensions and Zeta Functions影響因子(影響力)
書目名稱Fractal Geometry, Complex Dimensions and Zeta Functions影響因子(影響力)學(xué)科排名
書目名稱Fractal Geometry, Complex Dimensions and Zeta Functions網(wǎng)絡(luò)公開度
書目名稱Fractal Geometry, Complex Dimensions and Zeta Functions網(wǎng)絡(luò)公開度學(xué)科排名
書目名稱Fractal Geometry, Complex Dimensions and Zeta Functions被引頻次
書目名稱Fractal Geometry, Complex Dimensions and Zeta Functions被引頻次學(xué)科排名
書目名稱Fractal Geometry, Complex Dimensions and Zeta Functions年度引用
書目名稱Fractal Geometry, Complex Dimensions and Zeta Functions年度引用學(xué)科排名
書目名稱Fractal Geometry, Complex Dimensions and Zeta Functions讀者反饋
書目名稱Fractal Geometry, Complex Dimensions and Zeta Functions讀者反饋學(xué)科排名
|
|
|
|Archiver|手機版|小黑屋|
派博傳思國際
( 京公網(wǎng)安備110108008328)
GMT+8, 2025-10-15 18:42
發(fā)表于 2025-3-21 18:33:09
