A Diophantine inequality with four prime variables.

Let N be a sufficiently large real number. In this paper, it is proved that, for 1 < c < 1 1 9 3 8 8 9 , the following Diophantine inequality | p 1 c + p 2 c + p 3 c + p 4 c − N | < log − 1 N is solvable in prime variables p 1 , p 2 , p 3 , p 4 , which improves the result of Mu [On a Diophantine inequality over primes, Adv. Math. (China)44(4) (2015) 621–637]. [ABSTRACT FROM AUTHOR]