Continued fractions with minimal remainders

2010/02/10 by Zhabitskaya, Elena
#11J70 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1002.2053

Abstract

Consider the representation of a rational number in the form, associated with "centered" Euclidean algorithm. We prove a new formula for the limit distribution function for sequences of rationals with bounded sum of partial quotients.

Related

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• The distribution of rationals in residue classes
• Renewal-type Limit Theorem for Continued Fractions with Even Partial Quotients
• Non-convex geometry of numbers and continued fractions
• Continued fraction expansions for complex numbers - a general approach