%0 eBook
%M Solr-EB000364105
%A Lapidus, Michel L.
%I Springer New York
%D 2013
%C New York, NY
%G English
%B Springer Monographs in Mathematics
%@ 9781461421764
%T Fractal Geometry, Complex Dimensions and Zeta Functions Geometry and Spectra of Fractal Strings
%U http://dx.doi.org/10.1007/978-1-4614-2176-4?nosfx=y
%7 2nd ed. 2013
%X ...The book is very well written and organized and the subject is very interesting and actually has many applications." —Nicolae-Adrian Secelean, Zentralblatt Key Features include: · The Riemann hypothesis is given a natural geometric reformulation in the context of vibrating fractal strings · Complex dimensions of a fractal string are studied in detail, and used to understand the oscillations intrinsic to the corresponding fractal geometries and frequency spectra · Explicit formulas are extended to apply to the geometric, spectral, and dynamical zeta functions associated with a fractal · Examples of such explicit formulas include a Prime Orbit Theorem with error term for self-similar flows, and a geometric tube formula · The method of Diophantine approximation is used to study self-similar strings and flows · Analytical and geometric methods are used to obtain new results