|Sep 14, 2018
|Maxim Sølund Kirsebom
|University of Hamburg
Abstract: In 1972 Galambos published an extreme value law for largest entries in continued fractions expansions. In fact, Doeblin had already proven a Poisson law for continued fractions in 1937, which implies the result of Galambos. But a gap was discovered in Doeblins proof and only filled around 1972 by Iosifescu. Interestingly, Iosifescu used aspects of Galambos' proof to fill this gap, hence all three mathematicians may reasonably be credited with the Poisson law.
In this talk I will first discuss these results and their proofs. Furthermore I will discuss recent work on proving similar results for complex continued fractions as defined by Hurwitz. Finally I will discuss which dynamical implications one might hope to deduce and which problems arise in the complex case compared to the real case. This is joint work with Seonhee Lim, Seoul National University.