On Kurzweil’s 0-1 Law in Inhomogeneous Diophantine Approximation – Dong Han Kim (Dongguk University)

Venue

Sala Conferenze (Puteano, Centro De Giorgi).

Abstract

We give a sufficient and necessary condition such that for almost all $s\in{\mathbb R}$ $$ \ \theta-s\<\psi(n)\qquad\text{for infinitely many}\ n\in{\mathbb N}, $$ where $\theta$ is fixed and $\psi(n)$ 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 myself. Moreover, we also discuss an analogue of our result in the field of formal Laurent series which has similar consequences. This is joint work with Michael Fuchs.

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