Fractal Geometry and Number Theory

Reviews of the first edition: "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 gaining insight into these rich areas either for its own sake or with a view to applications. They will find it a stimulating guide, well written in a clear and pleasant style."
-Mathematical Reviews
"The new approach and results on the important problems illuminated in this work will appeal to researchers and graduate students in number theory, fractal geometry, dynamical systems, spectral geometry, and mathematical physics."
-Simulation News Europe
"It is the reviewer's opinion that the authors have succeeded in showing that the complex dimensions provide a very natural and unifying mathematical framework for investigating the oscillations in the geometry and the spectrum of a fractal string. The book is well written. The exposition is self-contained, intelligent and well paced."
-Bulletin of the London Mathematical Society
New to the second edition: * Material on Diophantine approximation of complex dimensions of nonlattice strings * Periodic orbits of self-similar flows * Discussion of connections between fractality and self-similarity in the non-lattice case. TOC:Overview * Preface to the Second Edition * Introduction * Complex
Dimensions of Ordinary Fractal Strings * Complex Dimensions of Self-
Similar Fractal Strings * Complex Dimensions of Nonlattice Self-
Similar Strings * Generalized Fractal Strings Viewed as Measures *
Explicit Formulas for Generalized Fractal Strings * Prime Orbits of
Self-Similar Flows * The Geometry and the Spectrum of Fractal Strings
* Tabular Neighborhoods and Minkowski Measurability * The Riemann
Hypothesis, Inverse Spectral Problems and Oscillatory Phenomena *
Generalized Cantor Strings and their Oscillations * The Critical Zeros
of Zeta Functions * Concluding Comments * Appendices * Zeta Functions
in Number Theory * Zeta Functions of Laplacians and Spectral
Asymptotics * References * Conventions * Symbol Index * Index * List
of Figures * Acknolwedgements