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On Kurzweil's 0-1 law in inhomogeneous Diophantine approximation

100%

Fuchs M., Kim D.

Acta Arithmetica

2016

tom 173

nr 1

41-57

We give a necessary and sufficient condition such that, for almost all s ∈ ℝ, ||nθ - s|| < ψ(n) for infinitely many n ∈ ℕ, where θ is fixed and ψ(n) is a positive, non-increasing sequence. This can be seen as a dual result to classical theorems of Khintchine and Szüsz which dealt with the situation where s is fixed and θ is random. Moreover, our result contains several earlier ones as special cases: two old theorems of Kurzweil, a theorem of Tseng and a recent result of the second author. We also discuss a similar result (with the same consequences) in the field of formal Laurent series.

Metric inhomogeneous Diophantine approximation on the field of formal Laurent series

100%

Kim D., Nakada H.

Acta Arithmetica

2011

tom 150

nr 2

129-142

Ograniczanie wyników

2 Acta Arithmetica

2 Kim D.

1 Fuchs M.

1 Nakada H.

1 2016

1 2011

Wyniki wyszukiwania

On Kurzweil's 0-1 law in inhomogeneous Diophantine approximation

Metric inhomogeneous Diophantine approximation on the field of formal Laurent series