A diophantine inequality with prime variables

Abstract

Let λ1, λ2, λ3 be non-zero reals, not all of the same sign and such that at least one ratio λi/λj is irrational. Then it is proved that for any given integer k ≥ 1 and real η, the inequaltiyis solvable for every ε > 0. More general and sharper results are also proved.