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Metrical limit theorems for maximal digits in complex continued fraction expansions

Maxim Kirsebom ⟨maximkirsebom@gmail.com⟩

Abstract:

Continued fractions have long been an object of interest to both number theorists and dynamicists. In the 1970’s and 80’s great progress was made on understanding metrical properties of continued fractions, i.e. measure-theoretic properties. A particular focus was on the the maximal digits of continued fractions and their properties. In this talk I will discuss some of these results including an extreme value law proved by Galambos and a Poisson Law by Iosifescu. I will also discuss some recent developments in the field, primarily generalisations of these results to complex continued fractions.

Status: Accepted

Collection: Dynamical Systems

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