11 citations · 24 across the 4 of their papers we have counts for
4 papers
Minkowski dimension and explicit tube formulas for -adic fractal strings
Michel L. Lapidus, Lũ' Hùng, Machiel van Frankenhuijsen
The local theory of complex dimensions describes the oscillations in the geometry (spectra and dynamics) of fractal strings. Such geometric oscillations can be seen most clearly in…
The Riemann Hypothesis for Function Fields over a Finite Field
Machiel van Frankenhuijsen
We discuss Enrico Bombieri's proof of the Riemann hypothesis for curves over a finite field. Reformulated, it states that the number of points on a curve $\C$ defined over the fini…
The ABC Theorem for Meromorphic Functions
Machiel van Frankenhuijsen
Using a `height-to-radical' identity, we define the archimedean contribution to the radical, $r_\arch$, and we give a new proof of the abc theorem for the field of meromorphic func…
Fractality, Self-Similarity and Complex Dimensions
Michel L. Lapidus, Machiel van Frankenhuijsen
We present an overview of a theory of complex dimensions of self-similar fractal strings, and compare this theory to the theory of varieties over a finite field from the geometric…