Irrationality and transcendence of continued fractions with algebraic integers

Simon Bruno Andersen, Simon Kristensen

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Abstract

We extend a result of Hančl, Kolouch and Nair on the irrationality and transcendence of continued fractions. We show that for a sequence {αn} of algebraic integers of degree bounded by d, each attaining the maximum absolute value among their conjugates and satisfying certain growth conditions, the condition (formula presented) implies that the continued fraction α = [0; α1, α2, . . . ] is not an algebraic number of degree less than or equal to D.

Original languageEnglish
JournalPublicationes mathematicae-Debrecen
Volume95
Issue3-4
Pages (from-to)469-476
Number of pages8
ISSN0033-3883
DOIs
Publication statusPublished - 2019

Keywords

  • Algebraic integers
  • Continued fractions
  • Irrationality
  • Transcendence

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