Kurzweil type metrical Diophantine properties in the field of formal Laurent series

Abstract

In this article, we consider Diophantine properties of the orbit of irrational rotations over the field of formal Laurent series F-q((X-1)). More precisely, for a given f is an element of F-q((X-1)) and a sequence (r(n)), we investigate the size of the set {g is an element of F-q((X-1)): [GRAPHICS] vertical bar{Qf} - g vertical bar < r(n) for infinitely many n is an element of N} in the sense of the Haar measure and the Hausdorff dimension. (c) 2013 Elsevier Inc. All rights reserved.