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Fractal Geometry, Complex Dimensions and Zeta Functions: Geometry and Spectra of Fractal Strings
Paperback
Series: Springer Monographs in Mathematics
ISBN13: 9781489988386
Publisher: Springer
Published: Oct 15 2014
Pages: 570
Weight: 1.81
Height: 1.21 Width: 6.14 Depth: 9.21
Language: English
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 is presented. The new final chapter discusses several new topics and results obtained since the publication of the first edition.
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, Second Edition will appeal to students and researchers in number theory, fractal geometry, dynamical systems, spectral geometry, and mathematical physics.
1 different editions
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Fractal Geometry, Complex Dimensions and Zeta Functions: Geometry and Spectra of Fractal Strings
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Lapidus, Michel L.
Fractal Geometry and Number Theory: Complex Dimensions of Fractal Strings and Zeros of Zeta Functions
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Fractal Geometry, Complex Dimensions and Zeta Functions: Geometry and Spectra of Fractal Strings
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Fractal Geometry and Number Theory: Complex Dimensions of Fractal Strings and Zeros of Zeta Functions
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