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Complex Continued Fractions and Extremal Theory (2401.00626v1)
Published 1 Jan 2024 in math.DS and math.NT
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 Fr\'echet 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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