Diophantine approximation and continued fraction expansions of algebraic power series in positive characteristic
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.
scientific article; zbMATH DE number 1048749