On Inhomogeneous Diophantine Approximation Original Research Article

A new approach to inhomogeneous Diophantine approximation is given and a method for the computation of inhomogeneous minima of binary quadratic forms is derived. The new method is simpler than earlier ones of Barnes and Swinnerton-Dyer. As an application, a new proof of a theorem of Davenport, which gives the complete sequence of inhomogeneous minima for the form x2 − xy − y2, is given.