New York Journal of Mathematics
Volume 18 (2012) 249-259


Alan Haynes

Inhomogeneous approximation by coprime integers

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Published: March 30, 2012
Keywords: Inhomogeneous Diophantine approximation
Subject: 11J20

This paper addresses a problem recently raised by Laurent and Nogueira about inhomogeneous Diophantine approximation with coprime integers. A corollary of our main theorem is that for any irrational α∈R and for any γ∈R and ε>0 there are infinitely many pairs of coprime integers m,n such that
|nα-m-γ |≦ 1/|n|1-ε.
This improves upon previously known results, in which the exponent of approximation was at best 1/2.


Research supported by EPSRC grant EP/J00149X/1.

Author information

School of Mathematics, University of Bristol, Bristol UK