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Continued fraction expansions of real algebraic numbers

Volume 188 / 2019

Xianzu Lin Acta Arithmetica 188 (2019), 325-343 MSC: Primary 11J70; Secondary 11J81. DOI: 10.4064/aa170610-28-6 Published online: 22 March 2019


We establish independence properties of continued fraction expansions of two algebraic numbers. Roughly speaking, if the continued fraction expansions of two irrational real algebraic numbers have the same long subword, then the two expansions have the same tails. If the two expansions have mirror symmetric long subwords, then both the algebraic numbers are quadratic. Applying the above results, we prove a theorem analogous to Roth’s theorem about approximation by algebraic numbers.


  • Xianzu LinCollege of Mathematics and Informatics
    Fujian Normal University
    350108, Fuzhou, China

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