Complex dimensions of self-similar fractal strings and Diophantine approximation.
Continued fractions, multidimensional diophantine approximations and applications
This paper is a brief review of some general Diophantine results, best approximations and their applications to the theory of uniform distribution.
Counting rational points near planar curves
We find an asymptotic formula for the number of rational points near planar curves. More precisely, if f:ℝ → ℝ is a sufficiently smooth function defined on the interval [η,ξ], then the number of rational points with denominator no larger than Q that lie within a δ-neighborhood of the graph of f is shown to be asymptotically equivalent to (ξ-η)δQ².