In this talk I will discuss some recent results concerning the
generalized Farey sequence. While these sequences arise naturally in the
study of discrete (and in particular thin) subgroups, they can be used to
describe interesting number theoretic sequences – for example rationals
whose continued fraction partial quotients are subject to congruence
conditions. Using methods from homogeneous dynamics we show that these
sequences equidistribute and that the local statistics converge. Moreover a
connection to Ford circle configurations allows us to extract very detailed
information concerning the gap distribution and Gauss-Kuzmin statistics for
one particular example of such a sequence.
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Last modified: April 08 2016 - 20:30:35