On a class of diophantine inequalities

Abstract

As a special case of more general results, it is proved in this note that, if α is any real number and δ any positive number, then there exists a positive integer X such that the inequalityhas infinitely many solutions in positive integers h and Yh.The method depends on the study of infinite sequences of real linear forms in a fixed number of variables. It has relations to that used by Kronecker in the proof of his classical theorem and can be generalised.