On Kurzweil's 0-1 Law in Inhomogeneous Diophantine Approximation

الأصل · EN

We give a sufficient and necessary condition such that for almost all s∈R nθ-s<ψ(n) infinitely manyn∈N, where θ is fixed and ψ(n) is a positive, non-increasing sequence. This improves upon an old result of Kurzweil and contains several previous results as special cases: two theorems of Kurzweil, a theorem of Tseng and a recent result of the second author. Moreover, we also discuss an analogue of our result in the field of formal Laurent series which has similar consequences.