A note on the Littlewood conjecture in positive characteristic

The main purpose of this note is to construct families of pairs of formal power series over a finite field, which satisfy the appropriate analogue of Littlewood's conjecture in Diophantine approximation. On the way, the continued fraction expansion, with linear pattern, of a family of formal po...

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Bibliographic Details
Published in:	Quaestiones mathematicae Vol. 43; no. 1; pp. 107 - 116
Main Author:	Ayadi, Khalil
Format:	Journal Article
Language:	English
Published:	Grahamstown Taylor & Francis 02-01-2020 Taylor & Francis Ltd
Subjects:	continued fractions Fields (mathematics) Finite fields formal power series Littlewood conjecture Power series
Online Access:	Get full text
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Summary:	The main purpose of this note is to construct families of pairs of formal power series over a finite field, which satisfy the appropriate analogue of Littlewood's conjecture in Diophantine approximation. On the way, the continued fraction expansion, with linear pattern, of a family of formal power series is given.
ISSN:	1607-3606 1727-933X
DOI:	10.2989/16073606.2018.1539047