Inhomogeneous Diophantine approximation of some Hurwitzian numbers

Richard T. Bumby, Mary E. Flahive

Published 2007-10-01Version 1

We continue the work of Takao Komatsu by considering the inhomogeneous approximation constant L(\theta,\phi) for Hurwitzian numbers \theta, and rationally related \phi(r \theta +m)/n in Q(\theta) +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 \theta,\phi for which L(\theta,\phi) is zero; consideration of small values of n^2 L(e^{2/s},\phi); and the proof of a conjecture of Komatsu.