Continued fraction expansions of algebraic numbers

In this paper we establish properties of independence for the continued fraction expansions of two algebraic numbers. Roughly speaking, if the continued fraction expansions of two irrational algebraic numbers have the same long sub-word, then the two continued fraction expansions have the same tails...

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Bibliographic Details
Main Author Lin, Xianzu
Format Journal Article
LanguageEnglish
Published 07.02.2017
Subjects
Mathematics - Number Theory
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Summary:In this paper we establish properties of independence for the continued fraction expansions of two algebraic numbers. Roughly speaking, if the continued fraction expansions of two irrational algebraic numbers have the same long sub-word, then the two continued fraction expansions have the same tails. If the two expansions have mirror symmetry long sub-words, then both the two algebraic numbers are quadratic. Applying the above results, we prove a theorem analogous to the Roth's theorem about approximation by algebraic numbers.
DOI:10.48550/arxiv.1702.01915