Screen LibraryFractal geometry, complex dimensions and zeta functions : geometry and spectra of fractal strings /
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 contex...
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| Main Authors: | |
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| Published: |
Springer,
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| Publisher Address: | New York : |
| Publication Dates: | 2013. |
| Literature type: | eBook |
| Language: | English |
| Edition: | Second edition. |
| Series: |
Springer monographs in mathematics
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| Subjects: | |
| Online Access: |
http://dx.doi.org/10.1007/978-1-4614-2176-4 |
| Summary: |
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 stringsComplex 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 spectraExplicit formulas are extended to apply to. |
| Carrier Form: | 1 online resource. |
| ISBN: |
9781461421764 (electronic bk.) 1461421764 (electronic bk.) |
| Index Number: | QA614 |
| CLC: | O189.3 |
| Contents: |
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 -- Fractal Tube Formulas -- Riemann Hypothesis and Inverse Spectral Problems -- Generalized Cantor Strings and their Oscillations -- Critical Zeros of Zeta Functions -- Fractality and Complex Dimensions -- New Results and Perspectives. |