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

共 39 条

[1] PRIMES OF THE FORM [N(C)]
BAKER, RC
HARMAN, G
RIVAT, J
[J]. JOURNAL OF NUMBER THEORY, 1995, 50 (02) : 261 - 277
[2] A ternary Diophantine inequality over primes
Baker, Roger
Weingartner, Andreas
[J]. ACTA ARITHMETICA, 2014, 162 (02) : 159 - 196
[3] Some applications of the double large sieve
Baker, Roger
Weingartner, Andreas
[J]. MONATSHEFTE FUR MATHEMATIK, 2013, 170 (3-4): : 261 - 304
[4] On a diophantine inequality involving prime numbers (III)
Cai, YC
[J]. ACTA MATHEMATICA SINICA-ENGLISH SERIES, 1999, 15 (03): : 387 - 394
[5] Cai YC., 1996, ACTA MATH SINICA, V39, P733
[6] A ternary Diophantine inequality involving primes
Cai, Yingchun
[J]. INTERNATIONAL JOURNAL OF NUMBER THEORY, 2018, 14 (08) : 2257 - 2268
[7] [曹晓东 Cao Xiao Dong], 2002, [数学学报, Acta Mathematica Sinica], V45, P361
[8] On the Waring-Goldbach problem with small non-integer exponent
Garaev, MZ
[J]. ACTA ARITHMETICA, 2003, 108 (03) : 297 - 302
[9] Graham SW., 1991, VANDERCORPUTS METHOD, DOI [10.1017/CBO9780511661976, DOI 10.1017/CBO9780511661976]
[10] Han X, 2021, J MATH-UK

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