Lapidus M.L., van Frankenhuysen M. Fractal Geometry and Number Theory: Complex Dimensions of Fractal Strings and Zeros of Zeta Functions

Basel: Birkhäuser, 2000. - 277 p.Complex Dimensions of Ordinary Fractal Strings
Complex Dimensions of Self-Similar Fractal Strings
Generalized Fractal Strings Viewed as Measures
Explicit Formulas for Generalized Fractal Strings
The Geometry and the Spectrum of Fractal Strings
Tubular 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