Quadratic Residues and Non-residues for Infinitely Many Piatetski-Shapiro Primes

被引：0
作者：
Ping XI [1 ]
机构：
[1] School of Mathematics and Statistics, Xi’an Jiaotong University
来源：
Acta Mathematica Sinica,English Series | 2013年 / 03期
基金：
中国国家自然科学基金; 中央高校基本科研业务费专项资金资助;
关键词：
Quadratic residue; quadratic non-residue; Piatetski-Shapiro prime;
D O I：
暂无
中图分类号：
O156 [数论];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we prove a quantitative version of the statement that every nonempty finite subset of N+ is a set of quadratic residues for infinitely many primes of the form [nc] with 1 ≤ c ≤243/205. Correspondingly, we can obtain a similar result for the case of quadratic non-residues under reasonable assumptions. These results generalize the previous ones obtained by Wright in certain aspects.
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收藏
页码：515 / 522
页数：8
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