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)
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