On Diophantine approximation with one prime and three squares of primes

摘要

Letλ1,λ2,λ3,λ4 be non-zero real numbers,not all of the same sign,(w) real.Suppose that the ratios λ1/λ2,λ1/λ3 are irrational and algebraic.Then there are infinitely many solutions in primes pj,j =1,2,3,4,to the inequality [λ1p1 + λ2p22 + λ3p2/3+ λ4p42 +(w)| ＜ (max{p1,p22,2p3,p4p2｝)-5/64.This improves the earlier result.