11 citations · 11 across the 1 of their papers we have counts for
3 papers
math.NT2008★ 1 cited
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…
math.NT2008★ 3 cited
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…
math.NT2004★ 11 cited
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…