Fractal Geometry, Complex Dimensions and Zeta Functions by Machiel van Frankenhuijsen
Fractal Geometry, Complex Dimensions and Zeta Functions: Geometry and Spectra of Fractal Strings (Springer Monographs in Mathematics) by Machiel van Frankenhuijsen
English | Aug 10, 2006 | ISBN: 0387332855 | 484 Pages | PDF | MB
English | Aug 10, 2006 | ISBN: 0387332855 | 484 Pages | PDF | MB
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.