Inhomogeneous Diophantine approximation of some Hurwitzian numbers

Richard T. Bumby; Mary E. Flahive

doi:10.1063/1.2841909

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arXiv · 0710.0399

Inhomogeneous Diophantine approximation of some Hurwitzian numbers

Richard T. Bumby·Mary E. Flahive

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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,ϕfor which L(θ,ϕ) is zero; consideration of small values of n^2 L(e^{2/s},ϕ); and the proof of a conjecture of Komatsu.

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Richard T. Bumby, Mary E. Flahive. 2007-10-01. Inhomogeneous Diophantine approximation of some Hurwitzian numbers. https://doi.org/10.1063/1.2841909

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