Fractal Geometry, Complex Dimensions and Zeta Functions: Geometry and Spectra of Fractal Strings
Language: English
Published by Springer Verlag, 2012
- Hardcover
- New

Seller: Revaluation Books, Exeter, United KingdomRevaluation Books
AbeBooks seller since January 6, 2003
Condition: New
£ 192.45
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2nd edition. 590 pages. 9.75x6.50x1.50 inches. In Stock.
Seller Inventory # x-1461421756
- Title
- Fractal Geometry, Complex Dimensions and Zeta Functions: Geometry and Spectra of Fractal Strings
- Author
- Lapidus, Michel L./ Van Frankenhuijsen, Machiel
- Publisher
- Springer Verlag
- Publication year
- 2012
- Condition
- Brand New
- Binding
- Hardcover
- Language
- English
- ISBN 10
- 1461421756
- ISBN 13
- 9781461421757
- Edition
- 2nd Edition
- Item weight
- 1.01 kilograms
- Series
- Book 94 of 187: Springer Monographs in Mathematics
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.
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Revaluation Books
Exeter, United Kingdom
AbeBooks seller since January 6, 2003
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