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Fractal geometry and number theory : complex dimensions of fractal strings and zeros of zeta functions

Author: Michel L Lapidus; Machiel Van Frankenhuysen
Publisher: Boston : Birkhäuser, ©2000.
Edition/Format:   Print book : EnglishView all editions and formats
Summary:

Number theory and fractal geometry are combined in this study of the vibrations of fractal strings. The book centres around a notion of complex dimension extended here to apply to the zeta functions  Read more...

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Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: Michel L Lapidus; Machiel Van Frankenhuysen
ISBN: 0817640983 9780817640989 3764340983 9783764340988
OCLC Number: 52404467
Description: x, 268 pages : illustrations ; 24 cm
Contents: 1. Complex Dimensions of Ordinary Fractal Strings --
2. Complex Dimensions of Self-Similar Fractal Strings --
3. Generalized Fractal Strings Viewed as Measures --
4. Explicit Formulas for Generalized Fractal Strings --
5. The Geometry and the Spectrum of Fractal Strings --
6. Tubular Neighbourhoods and Minkowski Measurability --
7. The Riemann Hypothesis, Inverse Spectral Problems and Oscillatory Phenomena --
8. Generalized Cantor Strings and their Oscillations --
9. The Critical Zeros of Zeta Functions --
10. Concluding Comments --
A. Zeta Functions in Number Theory --
B. Zeta Functions of Laplacians and Spectral Asymptotics.
Responsibility: Michel L. Lapidus, Machiel van Frankenhuysen.

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"This highly original self-contained book will appeal to geometers, fractalists, mathematical physicists and number theorists, as well as to graduate students in these fields and others interested in Read more...

 
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