A note on Diophantine approximation by unlike powers of primes

被引:11
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
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
收藏
页码:1651 / 1668
页数:18
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