A refined Kurzweil type theorem in positive characteristic

Abstract

We consider a Kurzweil type inhomogeneous Diophantine approximation theorem in the field of the formal Laurent series for a monotone sequence of approximation. We find a necessary and sufficient condition for irrational f and monotone increasing (l(n)) that there are infinitely many polynomials P and Q such that vertical bar Qf - P - g vertical bar < q(-n-ln), n = deg(Q) for almost every g. We also study some conditions for irrational f such that for all monotone increasing (l(n)) with Sigma q(-ln) = infinity there are infinitely many solutions for almost every g. (C) 2012 Elsevier Inc. All rights reserved.