A note on the Littlewood conjecture in positive characteristic

Abstract

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.

Mathematics Subject Classification (2010): 11J61, 11J70, 11K60.

Keywords: Finite fields, formal power series, continued fractions, Littlewood conjecture