Fractal Geometry and Number Theory: Complex Dimensions of Fractal Strings and Zeros of Zeta Functions

by Michel L. Lapidus

Can one hear the shape of a drum? The relationship between the shape (geometry) of a drum and its sound (its spectrum is an interesting and difficult problem to describe. In this monograph, an extensive study is made of this problem for one-dimensional drums with fractal strings. The work centers around the author's original research on a newly developed theory of "complex dimensions of fractal strings." All of the material is self-contained and provide a unique geometric characterization of the Riemann hypothesis.

284 pages, Paperback

First published December 10, 1999