Technical Fractal Geometry, Complex Dimensions and Zeta Functions: Geometry and Spectra of Fractal Strings (0387332855)

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Michel L. Lapidus, Machiel van Frankenhuijsen, "Fractal Geometry, Complex Dimensions and Zeta Functions: Geometry and Spectra of Fractal Strings"

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.

The significant studies and problems illuminated in this work may be used in a classroom setting at the graduate level. Fractal Geometry, Complex Dimensions and Zeta Functions will appeal to students and researchers in number theory, fractal geometry, dynamical systems, spectral geometry, and mathematical physics.

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	Science/Engineering The Fractal Geometry of Nature Benoit B. Mandelbrot, "The Fractal Geometry of Nature"W. H. Freeman \| ISBN: 0716711869 \| August 15, 1982 \| DJVU \| 480 pages \| 7278 KB “Imagine an equilateral triangle. Now, imagine smaller equilateral triangles perched in the center o ...
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	Fractal Geometry, Complex Dimensions and Zeta Functions: Geometry and Spectra of Fractal Strings (Springer Monographs in Mathematics) Author: Machiel van Frankenhuijsen, Michel L. LapidusPublisher: Springer (2006)Binding: Hardcover, 464 pagespricer: $54.95ISBN-10: 0387332855editorialreviewsNumber theory, spectral geometry, and fractal geometry are interlinked in this in-d ...

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	Science/Engineering The Fractal Geometry of Nature Benoit B. Mandelbrot, "The Fractal Geometry of Nature"W. H. Freeman \| ISBN: 0716711869 \| August 15, 1982 \| DJVU \| 480 pages \| 7278 KB “Imagine an equilateral triangle. Now, imagine smaller equilateral triangles perched in the center o ...
	Science/Engineering Techniques in Fractal Geometry Kenneth Falconer " Techniques in Fractal Geometry" Wiley \| 1997-04-28 \| ISBN: 0471957240 \| 274 pages \| Djvu \| 1,93 MB Following on from the success of Fractal Geometry: Mathematical Foundations and Applications, this new sequel presents ...
	Measure, Topology, and Fractal Geometry Gerald Edgar, "Measure, Topology, and Fractal Geometry" Springer \| 2007-11-26 \| ISBN: 0387747486 \| 272 pages \| PDF \| 4,9 MB "In the world of mathematics, the 1980's might well be described as the "decade of the fractal". Starting with B ...
	Science/Engineering Fractal Geometry: Mathematical Foundations and Applications Kenneth Falconer, "Fractal Geometry: Mathematical Foundations and Applications"Wiley \| 2003-11-14 \| ISBN: 0470848618 \| 366 pages \| PDF \| 2,5 MBSince its original publication in 1990, Kenneth Falconer's Fractal Geometry: Mathematical Foundat ...
	Fractal Geometry and Stochastics IV Fractal Geometry and Stochastics IV Publisher: Birkhäuser Basel \| 290 pages \| September 18, 2009 \| ISBN 3034600291 \| PDF \| 4 MBOver the last fifteen years fractal geometry has established itself as a substantial mathematical theory in its ...
	Fractal Geometry, Complex Dimensions and Zeta Functions: Geometry and Spectra of Fractal Strings (Springer Monographs in Mathematics) Author: Machiel van Frankenhuijsen, Michel L. LapidusPublisher: Springer (2006)Binding: Hardcover, 464 pagespricer: $54.95ISBN-10: 0387332855editorialreviewsNumber theory, spectral geometry, and fractal geometry are interlinked in this in-d ...

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