Download or read book Fractal Geometry, Complex Dimensions and Zeta Functions written by Michel L. Lapidus and published by Springer Science & Business Media. This book was released on 2007-08-08 with total page 472 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.