BGU SEMINAR IN PROBABILITY AND ERGODIC THEORY Shalom all, SPEAKER: Menny Aka, Hebrew University DATE: 19.12.10 TIME: 14:00 PLACE: Seminar room -101 TITLE: On the Continued fraction expansion of quadratic irrationals ABSTRACT: It is well known that quadratic irrationals are characterized as the numbers whose continued fraction expansion is eventually periodic. Each quadratic irrational exhibits then a certain statistics in its period (for example, one can measure the frequency of the digit 1 in the period). I will present a recent result regarding the continued fraction expansionsof certain sequences of quadratic irrationals. We prove the following Theorem: Let x be a quadratic irrational and p a prime. Then the statistics of the period of the continued fraction expansion of p^nx converges to the "right" statistics; i.e. to the one given by the Gauss-Kuzmin measure. Our proof exploits a classical connection between the continued fraction expansion and dynamics on the modular surface. I will review this connection and explain the proof of an equivalent equidistribution result on a S-arithmetic homogeneous space. This is joint work with U. Shapira. --------------------------------------------------------- Technion Math Net-2 (TECHMATH2) Editor: Michael Cwikel <techm@math.technion.ac.il> Announcement from: Barak Weiss <barakw@cs.bgu.ac.il>