Fractal Geometry, Complex Dimensions and Zeta Functions

Name: Fractal Geometry, Complex Dimensions and Zeta Functions
SKU: 22909255
Price: 433.00 NZD
Availability: InStock

Geometry and Spectra of Fractal Strings

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Format:

Paperback / softback

Series:

Springer Monographs in Mathematics

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$433.00

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Description

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.

Release date NZ

October 15th, 2014

Author

Audiences

Postgraduate, Research & Scholarly
Professional & Vocational

Edition

2nd ed. 2013

Illustrations

XXVI, 570 p.

Pages

570

Series

Springer Monographs in Mathematics

Dimensions

155x235x31

ISBN-13

9781489988386

Product ID

22909255

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