Inhomogeneous Diophantine approximation of some Hurwitzian numbers
Abstract
We continue the work of Takao Komatsu by considering the inhomogeneous approximation constant L(θ,φ) for Hurwitzian numbers θ, and rationally related φ(r θ +m)/n in 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) is zero; consideration of small values of n2 L(e2/s,φ); and the proof of a conjecture of Komatsu.
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