Paper
Asymptotic statistics for finite continued fractions with restricted digits
Authors
Jungwon Lee
Abstract
Zaremba's conjecture concerns a formation of continued fraction expansions for rational numbers with partial quotient bounded by an absolute constant. We present asymptotic estimates for the size of -thickening of certain fractal sets of bounded-type, which in turn provide additional support for Zaremba's conjecture on average. We also conclude a generalisation for complex continued fractions over imaginary quadratic fields.