Classification and symmetries of a family of continued fractions with bounded period length

Kell Hiu Fai CHENG, Richard K. GUY, Renate SCHEIDLER, Hugh C. WILLIAMS

Research output: Contribution to journalArticles

Abstract

It is well known that the regular continued fraction expansion of a quadratic irrational is symmetric about its centre; we refer to this symmetry as horizontal. However, an additional vertical symmetry is exhibited by the continued fraction expansions arising from a family of quadratics known as Schinzel sleepers. This paper provides a method for generating every Schinzel sleeper and investigates their period lengths as well as both their horizontal and vertical symmetries. Copyright © 2013 Australian Mathematical Publishing Association Inc.
Original languageEnglish
Pages (from-to)53-76
JournalJournal of the Australian Mathematical Society
Volume93
Issue number1/2
DOIs
Publication statusPublished - Oct 2012

Citation

Cheng, K. H. F., Guy, R. K., Scheidler, R., & Williams, H. C. (2012). Classification and symmetries of a family of continued fractions with bounded period length. Journal of the Australian Mathematical Society, 93(1/2), 53-76.

Keywords

  • Continued fraction expansion
  • Period length
  • Schinzel sleeper

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