A refined Kurzweil type theorem in positive characteristic

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 (^ℓn) that there are infinitely many polynomials P and Q such that |Qf-P-g|<q-ⁿ-^ℓn, n=deg(Q) for almost every g. We also study some conditions for irrational f such that for all monotone increasing (^ℓn) with Σq- ^ℓn=∞ there are infinitely many solutions for almost every g.