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,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.

Diophantine Analysis and Related Fields 2007, Keio University, Japan