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arXiv · 2202.07976

Extreme Value Theory for Hurwitz Complex Continued Fractions

Maxim Kirsebom
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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.

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Maxim Kirsebom. 2022-02-16. Extreme Value Theory for Hurwitz Complex Continued Fractions. https://doi.org/10.3390/e23070840

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