A Note on Inhomogeneous Diophantine Approximation With a General Error Function

Abstract

Abstract. Let α be an irrational number and ϕ: ‫ގ‬ → ‫ޒ‬ + be a decreasing sequence tending to zero. Consider the setwhere · denotes the distance to the nearest integer. We show that for general error function ϕ, the Hausdorff dimension of E ϕ (α) depends not only on ϕ, but also heavily on α. However, recall that the Hausdorff dimension of E ϕ (α) is independent of α when ϕ(n) = n −γ with γ > 1.2000 Mathematics Subject Classification. 11J83, 28A80.

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