Analysseminarium, Maxim Kirsebom, "Metrical limit theorems for maximal digits in continued fraction expansions"
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Analysseminarium, Maxim Kirsebom, Hamburg.
"Metrical limit theorems for maximal digits in continued fraction
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, a Poisson Law
by Iosifescu and a rate of convergence result by Philipp. I will also discuss
some recent developments in the field including generalisations of these results
to complex continued fractions as well as an improvement on the rate of
convergence to an extreme value law. These results are joint work with Seonhee
Lim and with Anish Ghosh and Parthanil Roy.