Diophantine Inequality by Unlike Powers of Primes

Li ZHU

1School of Statistics and Mathematics,Shanghai Lixin University of Accounting and Finance,Shanghai 201209,China.E-mail:shulunz@163.com

Abstract Suppose that λ1,··· ,λ5 are nonzero real numbers,not all of the same sign,satisfying that is irrational.Then for any given real number η and ε>0,the inequality

has infinitely many solutions in prime variables p1,··· ,p5.This result constitutes an improvement of the recent results.

Keywords Prime,Davenport-Heilbronn method,Diophantine inequalities

1 Introduction

2 Outline of the Method

3 Some Auxiliary Lemmas

4 The Minor Arc m

5 Proof of Theorem 1.1