Two Diophantine Inequalities over Primes with Fractional Power

被引：1

作者：

Liu, Huafeng ^{[1
]}

机构：

[1] Shandong Normal Univ, Sch Math & Stat, Jinan 250014, Peoples R China

来源：

FRONTIERS OF MATHEMATICS | 2023年 / 18卷 / 06期

基金：

中国国家自然科学基金;

关键词：

Diophantine inequality; exponential sum; prime; NUMBERS;

D O I：

10.1007/s11464-021-0260-y

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let 1 < c < (256) /(119), c not equal 2 and N be a sufficiently large real number. In this paper, we first prove that the Diophantine inequality |p (c)(1)+p (c)(2)+<middle dot> <middle dot> <middle dot>+p (c)(6)-N| < log(-1) N is solvable in primes p1, p2, ... , p6. Moreover, we prove that for almost all R is an element of (N, 2N], the Diophantine inequality |p (c)(1)+ p (c)(2 )+ p (c)(3) - R| < log(-1) N is solvable in primes p1, p2, p3. These results constitute further improvements upon previous results.

引用

页码：1349 / 1362

页数：14

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