Fractal Geometry, Complex Dimensions and Zeta Functions
Springer-Verlag New York Inc.
978-0-387-33285-7 (ISBN)
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Number theory, spectral geometry, and fractal geometry are interlinked in this study of the vibrations of fractal strings, that is, one-dimensional drums with fractal boundary. The Riemann hypothesis is given a natural geometric reformulation in context of vibrating fractal strings, and the book offers explicit formulas extended to apply to the geometric, spectral and dynamic zeta functions associated with a fractal.
List of Figures.- Preface.- Overview.- Introduction.- Complex Dimensions of Ordinary Fractal Strings.- Complex Dimensions of Self-Similar Fractal Strings.- Complex Dimensions of Nonlattice Self-Similar Strings: Quasiperiodic Patterns and Diophantine Approximation.- Generalized Fractal Strings Viewed as Measures.- Explicit Formulas for Generalized Fractal Strings.- The Geometry and the Spectrum of Fractal Strings.- Periodic Orbits of Self-Similar Flows.- Tubular Neighborhoods and Minkowski Measurability.- The Riemann Hypothesis and Inverse Spectral Problems.- Generalized Cantor Strings and their Oscillations.- The Critical Zeros of Zeta Functions.- Concluding Comments, Open Problems, and Perspectives.- Appendices.- A. Zeta Functions in Number Theory.- B. Zeta Functions of Laplacians and Spectral Asymptotics.- C. An Application of Nevanlinna Theory.- Bibliography.- Acknolwedgements.- Conventions.- Index of Symbols.- Author Index.- Subject Index.
| Erscheint lt. Verlag | 12.9.2006 |
|---|---|
| Reihe/Serie | Springer Monographs in Mathematics |
| Zusatzinfo | 1, black & white illustrations |
| Verlagsort | New York, NY |
| Sprache | englisch |
| Maße | 156 x 234 mm |
| Gewicht | 857 g |
| Einbandart | gebunden |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik |
| Naturwissenschaften ► Physik / Astronomie | |
| ISBN-10 | 0-387-33285-5 / 0387332855 |
| ISBN-13 | 978-0-387-33285-7 / 9780387332857 |
| Zustand | Neuware |
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