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

被引：1
|
作者：
Xi, Ping [1 ]
机构：
[1] Xi An Jiao Tong Univ, Sch Math & Stat, Xian 710049, Peoples R China
来源：
ACTA MATHEMATICA SINICA-ENGLISH SERIES | 2013年 / 29卷 / 03期
基金：
中国国家自然科学基金;
关键词：
Quadratic residue; quadratic non-residue; Piatetski-Shapiro prime; NUMBERS;
D O I：
10.1007/s10114-012-1227-4
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
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 [n(c)] 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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页码：515 / 522
页数：8
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