A note on Diophantine approximation by unlike powers of primes

被引：12

作者：

Mu, Quanwu ^{[1
]}

Qu, Yunyun ^{[2
]}

机构：

[1] Xian Polytech Univ, Sch Sci, Xian 710048, Shaanxi, Peoples R China

[2] Guizhou Normal Univ, Sch Math Sci, Guiyang 550001, Guizhou, Peoples R China

来源：

INTERNATIONAL JOURNAL OF NUMBER THEORY | 2018年 / 14卷 / 06期

基金：

中国国家自然科学基金;

关键词：

Diophantine inequality; prime; Davenport-Heilbronn method; TERNARY QUADRATIC-FORMS; BINARY LINEAR-FORMS; 3; SQUARES; NUMBERS; ARGUMENTS; VALUES; SUMS; INEQUALITIES; VARIABLES;

D O I：

10.1142/S1793042118501002

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

It is proved that if lambda(1), lambda(2), . . . , lambda(5) are nonzero real numbers, not all of the same sign and lambda(1)/lambda(2) is irrational, then for given real numbers eta and sigma, 0 < sigma < 5/252, 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 infinitely many solutions in prime variables p(1), p(2), p(3), p(4), p(5). This result constitutes an improvement upon that of Liu for the range 0 < sigma < 5/288.

引用

页码：1651 / 1668

页数：18

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