Continued fraction algorithms and Lagrange's theorem in \mathbb Q_p

2017/01/17 by Asaki Saito, Saito, Asaki, Jun-ichi Tamura +3
Mathematics · Computer Science · #Mathematical Dynamics and Fractals #semigroups and automata theory #Coding theory and cryptography

paper · pdf · doi:10.48550/arxiv.1701.04615

Abstract

We present several continued fraction algorithms, each of which gives an eventually periodic expansion for every quadratic element of \mathbb Q_p over \mathbb Q and gives a finite expansion for every rational number. We also give, for each of our algorithms, the complete characterization of elements having purely periodic expansions.

Related

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• On the periodicity of an algorithm for p-adic continued fractions