The question of q, a look at the interplay of number theory and ergodic theory in continued fractions

Speaker: Joseph Vandehey

Date: Wed, Nov 16, 2022

Location: Online

Conference: University of Utah Seminar in Ergodic Theory

Subject: Mathematics

Class: Scientific


In the theory of continued fractions, the denominator of the truncated fraction (often denoted q) contains a great deal of information important in applications. However, q is a surprisingly complicated object from the point of view of ergodic theory. We will look at a few problems related to q and see how different techniques have overcome these difficulties, including modular properties (Moeckel, Fisher-Schmidt), renewal-type theorems (Sinai-Ulcigrai, Ustinov), and "nonstandard" arrangements of points (Avdeeva-Bykovskii).