Diophantine approximation and continued fraction expansions of algebraic power series in positive characteristic
type: Item
instance of: scholarly article
title: Diophantine approximation and continued fraction expansions of algebraic power series in positive characteristic
zbMATH Open document ID: 0874.11051
author: Alain Lasjaunias
published in: Journal of Number Theory
publication date: 1997-08-17T00:00:00Z
review text: The author finds the continued fraction expansion of some algebraic functions in characteristic \(p\). This allows him to deduce diophantine approximation properties of these algebraic functions. He recovers some interesting examples of \textit{M. W. Buck} and \textit{D. P. Robbins} [J. Number Theory 50, 335-344 (1995; Zbl 0822.11051)] and adds some more of his own. These are examples where the analogue of Roth's theorem holds but the partial quotients are unbounded. Finally, he gives the continued fraction expansion of a famous example of Mahler's for which Roth's theorem fails and in fact the Liouville bound is best possible.
Mathematics Subject Classification ID: 11J61
Mathematics Subject Classification ID: 11J70
zbMATH DE Number: 1048749
zbMATH Keywords: diophantine approximation
zbMATH Keywords: continued fractions
zbMATH Keywords: characteristic \(p\)
reviewed by: José Felipe Voloch
MaRDI profile type: Publication
full work available at URL: jnth.1997.2160
OpenAlex ID: W2055305178
cites work: Continued fractions of algebraic power series in characteristic 2
cites work: The continued fraction expansion of an algebraic power series satisfying a quartic equation
cites work: Thue's Theorem in positive characteristic.
cites work: On a Theorem of Liouville in Fields of Positive Characteristic
cites work: Approximation exponents for algebraic functions in positive characteristic
cites work: Continued fractions for certain algebraic power series
cites work: Diophantine approximation in positive characteristic
cites work: Diophantine approximation in characteristic \(p\)
DOI: 10.1006/JNTH.1997.2160
description: scientific article; zbMATH DE number 1048749