 

Alan Haynes
Inhomogeneous approximation by coprime integers view print


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


Abstract
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
nαmγ ≦ 1/n^{1ε}.
This improves upon previously known results, in which the exponent of approximation was at best 1/2.


Acknowledgements
Research supported by EPSRC grant EP/J00149X/1.


Author information
School of Mathematics, University of Bristol, Bristol UK
alan.haynes@bristol.ac.uk

