Fractal Geometry, Complex Dimensions and Zeta Functions

1. Introduction

2. Complex Dimensions of Ordinary Fractal Strings

3. Complex Dimensions of Self-Similar Fractal Strings

4. Complex Dimensions of Nonlattice Self-Similar Strings: Quasiperiodic Patterns and Diophantine Approximation

5. Generalized Fractal Strings Viewed as Measures

6. Explicit Formulas for Generalized Fractal Strings

7. The Geometry and the Spectrum of Fractal Strings

8. Periodic Orbits of Self-Similar Flows

9. Tubular Neighborhoods and Minkowski Measurability

10. The Riemann Hypothesis and Inverse Spectral Problems

11. Generalized Cantor Strings and their Oscillations

12. The Critical Zeros of Zeta Functions

13. Concluding Comments, Open Problems, and Perspectives

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Avainsanat: MATHEMATICS / General MAT000000