The Inhomogeneous Hall's Ray

Details The Inhomogeneous Hall's Ray The Inhomogeneous Hall's Ray

2012-03-20

arxiv.org/abs/1203.4295v2

Mathematics

Number Theory

Fixed typos and pictures

Scientific paper

We show that the inhomogenous approximation spectrum, associated to an
irrational number \alpha\ always has a Hall's Ray; that is, there is an
\epsilon>0 such that [0,\epsilon) is a subset of the spectrum. In the case when
\alpha\ has unbounded partial quotients we show that the spectrum is just a
ray.

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