Extreme Value Theory for Hurwitz Complex Continued Fractions

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 o...

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Autor principal: Kirsebom, Maxim Sølund
Formato: Online Artículo Texto
Lenguaje:English
Publicado: MDPI 2021
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8303893/
https://www.ncbi.nlm.nih.gov/pubmed/34209005
http://dx.doi.org/10.3390/e23070840
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author Kirsebom, Maxim Sølund
author_facet Kirsebom, Maxim Sølund
author_sort Kirsebom, Maxim Sølund
collection PubMed
description 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 obtained several results concerning the extremes of nearest integer continued fractions as well.
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spelling pubmed-83038932021-07-25 Extreme Value Theory for Hurwitz Complex Continued Fractions Kirsebom, Maxim Sølund Entropy (Basel) Article 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 obtained several results concerning the extremes of nearest integer continued fractions as well. MDPI 2021-06-30 /pmc/articles/PMC8303893/ /pubmed/34209005 http://dx.doi.org/10.3390/e23070840 Text en © 2021 by the author. https://creativecommons.org/licenses/by/4.0/Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).
spellingShingle Article
Kirsebom, Maxim Sølund
Extreme Value Theory for Hurwitz Complex Continued Fractions
title Extreme Value Theory for Hurwitz Complex Continued Fractions
title_full Extreme Value Theory for Hurwitz Complex Continued Fractions
title_fullStr Extreme Value Theory for Hurwitz Complex Continued Fractions
title_full_unstemmed Extreme Value Theory for Hurwitz Complex Continued Fractions
title_short Extreme Value Theory for Hurwitz Complex Continued Fractions
title_sort extreme value theory for hurwitz complex continued fractions
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8303893/
https://www.ncbi.nlm.nih.gov/pubmed/34209005
http://dx.doi.org/10.3390/e23070840
work_keys_str_mv AT kirsebommaximsølund extremevaluetheoryforhurwitzcomplexcontinuedfractions

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