Extreme Value Theory for Hurwitz Complex Continued Fractions
Number Theory
2022-02-17 v1 Dynamical Systems
Probability
Abstract
The Hurwitz complex continued fraction is a generalization of the nearest integer continued fraction. In this paper we prove various results concerning extremes of the modulus of Hurwitz complex continued fraction digits. This includes a Poisson law and an extreme value law. The results are based on cusp estimates of the invariant measure about which information is still limited. In the process, we get several results concerning extremes of nearest integer continued fractions as well.
Cite
@article{arxiv.2202.07976,
title = {Extreme Value Theory for Hurwitz Complex Continued Fractions},
author = {Maxim Kirsebom},
journal= {arXiv preprint arXiv:2202.07976},
year = {2022}
}
Comments
15 pages, 3 figures