Diophantine approximation with one prime and three squares of primes

被引：12

作者：

Li, Weiping ^{[1
]}

Wang, Tianze ^{[2
]}

机构：

[1] Henan Univ Finance & Econ, Dept Math & Informat Sci, Zhengzhou 450002, Peoples R China

[2] N China Univ Water Conservancy & Elect Power, Sch Math & Informat Sci, Zhengzhou 450011, Peoples R China

来源：

RAMANUJAN JOURNAL | 2011年 / 25卷 / 03期

基金：

中国国家自然科学基金;

关键词：

Diophantine approximation; Prime; Davenport-Heilbronn method; NUMBERS; SUMS;

D O I：

10.1007/s11139-010-9290-x

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We show that if lambda(1), lambda(2), lambda(3), lambda(4) are nonzero real numbers, not all of the same sign, eta is real, and at least one of the ratios lambda(1)/lambda(j) (j = 2, 3, 4) is irrational, then given any real number omega > 0, there are infinitely many ordered quadruples of primes (p(1), p(2), p(3), p(4)) for which |lambda(1)p(1) + lambda(2)p(2)(2) + lambda(3)p(3)(2) + lambda(4)p(4)(2) + eta| < (max p(j))(-1/28+omega).

引用

页码：343 / 357

页数：15

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