Complex continued fractions, Kleinian and extremal theory for cusp excursions

2024/01/01 by Alexander Baumgärtner, Baumgartner, Alexander, Mark Pollicott +1
Mathematics · #28D05 #Analytic Number Theory Research #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Mathematical and Theoretical Analysis #Number Theory (math.NT) #Primary 37D40 #Secondary 11K50

paper · pdf · doi:10.48550/arxiv.2401.00626

openalex publication_date 2024/01/01 · openalex created_date 2024/01/03 · openalex updated_date 2026/08/03

Abstract

For the each of the five Euclidean rings of complex quadratic integers, we consider a complex continued fraction algorithm with digits in the ring. We show for each algorithm that the maximal digit obeys a Fréchet distribution. We use this to find a limiting distribution for cusp excursions on Bianchi orbifolds associated with the aforementioned rings of quadratic integers.

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