Diophantine inequalities over Piatetski-Shapiro primes

被引：1

作者：

Huang, Jing ^{[1
]}

Zhai, Wenguang ^{[2
]}

Zhang, Deyu ^{[1
]}

机构：

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

[2] China Univ Min & Technol, Dept Math, Beijing 100083, Peoples R China

来源：

FRONTIERS OF MATHEMATICS IN CHINA | 2021年 / 16卷 / 03期

基金：

中国国家自然科学基金;

关键词：

Diophantine inequalities; Piatetski-Shapiro primes; exponential sums; additive problems; NUMBER; APPROXIMATION;

D O I：

10.1007/s11464-021-0916-7

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let c > 1 and 0 < gamma < 1. We study the solubility of the Diophantine inequality divide p1(c) + p2(c) + horizontal ellipsis + ps(c)- N divide < (log N)(- 1) in Piatetski-Shapiro primes p(1), p(2), horizontal ellipsis , p(s) of the form p(j) = [m(1/gamma)] for some m is an element of N, and improve the previous results in the cases s = 2, 3, 4.

引用

页码：749 / 770

页数：22

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