Vol. 90, No. 2, 1980

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On linear forms and Diophantine approximation

Jeffrey D. Vaaler

Vol. 90 (1980), No. 2, 475–482
Abstract

Let x be a vector in Rk and let Λj(x), j = 1,2,,J be J linear forms in K variables. We prove that there is a lattice point u in Zk, u0, for which |Λj(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
Authors
Jeffrey D. Vaaler
Department of Mathematics
University of Texas at Austin
1 University Station - C1200
Austin TX 78712-0257
United States