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

By Michel L. Lapidus, M. V. Frankenhuysen. 2005

140 citations recorded by the source corpus.

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

Dimensions and singular traces for spectral triples, with applications to fractals (2002, background): “Indeed this class, or better the class of their complements, the so called fractal strings, constituted the first playground of the analysis of Lapidus and collaborators [29].”
Fractal Geometry and Applications: A Jubilee of Benoît Mandelbrot (2004, background): “, the relevant references in [La2]–[La4] and [La-vF]).”
The notion of dimension in geometry and algebra (2005, background): “ts and calculate their spectra. Even more straightforward constructions can be given for special fractal sets like fractal strings or generalized fractal strings of Lapidus and van Frankenhuysen, cf. [LavF2], Ch. 3. Sometimes it turns out that that the whole spectrum lies on the line Res= D 0, where”