One Diophantine inequality with unlike powers of prime variables

被引：12

作者：

Ge, Wenxu ^{[1
]}

Li, Weiping ^{[2
]}

机构：

[1] North China Univ Water Resources & Elect Power, Dept Math & Informat Sci, Zhengzhou 450046, Peoples R China

[2] Henan Univ Econ & Law, Dept Math & Informat Sci, Zhengzhou 450046, Peoples R China

来源：

JOURNAL OF INEQUALITIES AND APPLICATIONS | 2016年

基金：

中国国家自然科学基金;

关键词：

Davenport-Heilbronn method; prime; Diophantine approximation; APPROXIMATION; NUMBERS;

D O I：

10.1186/s13660-016-0983-6

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we show that if lambda(1), lambda(2), lambda(3), lambda(4), lambda(5) are nonzero real numbers not all of the same sign, eta is real, 0 < sigma < 1/720, and at least one of the ratios lambda(i)/lambda(j) (1 <= i < j <= 5) is irrational, then the inequality vertical bar lambda(1)p(1) +lambda(2)p(2)(2) + lambda(3)p(3)(3) + lambda(4)p(4)(4) + lambda(5)p(5)(5) +eta vertical bar < (max(1 <= j <= 5) p(j)(j))(-sigma) has infinite solutions with primes p(1), p(2), p(3), p(4), p(5).

引用

页码：1 / 8

页数：8