The continued fractions ladder of (√[3]m,√[3]m²)

2011/07/30 by Mitja Lakner, Lakner, Mitja, Peter Petek +3
Computer Science · Mathematics · #Advanced Mathematical Identities #FOS: Mathematics #Mathematical Dynamics and Fractals #Number Theory (math.NT) #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.1108.0087

openalex publication_date 2011/07/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Quadratic irrationals posses a periodic continued fraction expansion. Much less is known about cubic irrationals. We do not even know if the partial quotients are bounded, even though extensive computations suggest they might follow Kuzmin's probability law. Results are given for sequences of partial quotients of √[3]m and √[3]m² with m noncube. A big partial quotient in one sequence finds a connection in the other.

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