Logic Seminar
Jan Reimann
Penn State University
Effective aspects of diophantine approximation
Abstract: Diophantine approximation studies how well real numbers can be approximated in terms of rational numbers (or more generally, algebraic numbers). One measure of approximability is the irrationality exponent -- the supremum of all numbers $r>0$ such that there exist infinite many rational numbers $p/q$ with $|x - p/q| < 1/{q^r}$.
Almost every number (with respect to Lebesgue measure) has irrationality exponent 2. In this talk, we present a new result that strengthens and effectivizes a classical theorem due to Jarnik and Besicovitch regarding the Hausdorff dimension of sets of reals with a fixed irrationality exponent.
Tuesday March 15, 2016 at 4:00 PM in SEO 427