Inhomogeneous Diophantine approximation of some Hurwitzian numbers

Abstract

We continue the work of Takao Komatsu, and consider the inhomogeneous approximation constant L(θ, φ) for Hurwitzian θ and φ ∈ Q(θ) + Q. The current work uses a compactness theorem to relate such inhomogeneous constants to the homogeneous approximation constants. Among the new results are: a characterization of such pairs θ, φ for which L(θ, φ) = 0, consideration of small values of n 2 L(e 2/s , φ) for φ = (rθ + m)/n, and the proof of a conjecture of Komatsu.