Fractal Geometry, Complex Dimensions and Zeta Functions

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. In this book The Riemann hypothesis is given a natural geometric reformulation in the context of vibrating fractal strings. The book also offers explicit formulas extended to apply to the geometric, spectral, and dynamic zeta functions associated with a fractal. In addition, numerous theorems, examples, remarks and illustrations enrich the text.