Bounded partial quotients of some cubic power series with binary coefficients

Khalil Ayadi; Salah Beldi; Kwankyu Lee

doi:10.4134/BKMS.b150402

Bulletin of the
Korean Mathematical Society BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2016; 53(4): 1005-1015

Printed July 31, 2016

https://doi.org/10.4134/BKMS.b150402

Bounded partial quotients of some cubic power series with binary coefficients

Khalil Ayadi, Salah Beldi, and Kwankyu Lee

University of Sfax, University of Sfax, Chosun University

Abstract

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Abstract

It is a surprising but now well-known fact that there exist algebraic power series of degree higher than two with partial quotients of bounded degrees in their continued fraction expansions, while there is no single algebraic real number known with bounded partial quotients. However, it seems that these special algebraic power series are quite rare and it is hard to determine their continued fraction expansions explicitly. To the short list of known examples, we add a new family of cubic power series with bounded partial quotients.

Keywords: power series, continued fraction, finite fields

MSC numbers: 11J61, 11J70