On linear forms and Diophantine approximation

Jeffrey D. Vaaler

Vol. 90 (1980), No. 2, 475–482

DOI: 10.2140/pjm.1980.90.475

Abstract

Let x be a vector in R^k and let Λ_j(x), j = 1,2,⋯,J be J linear forms in K variables. We prove that there is a lattice point u in Z^k, u≠0, for which |Λ_j(u)| are all small (or zero) and the components of u are not too large. The bounds that we obtain improve several previous results on this problem.

Mathematical Subject Classification

Primary: 10F35, 10F35

Secondary: 10F37, 10E99

Milestones

Received: 1 June 1979

Published: 1 October 1980