The Quadratic Residues and Some of Their New Distribution Properties

被引：8
|
作者：
Wang, Tingting [1 ]
Lv, Xingxing [2 ]
机构：
[1] Northwest A&F Univ, Coll Sci, 22 Xinong Rd, Yangling 712100, Shaanxi, Peoples R China
[2] Northwest Univ, Sch Math, Xian 710127, Peoples R China
来源：
SYMMETRY-BASEL | 2020年 / 12卷 / 03期
关键词：
quadratic residues; quadratic non-residues; Legendre's symbol; character sums; asymptotic formula; NONRESIDUES;
D O I：
10.3390/sym12030421
中图分类号：
O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];
学科分类号：
07 ; 0710 ; 09 ;
摘要：
In this paper, we give some interesting identities and asymptotic formulas for one kind of counting function, by studying the computational problems involving the symmetry sums of one kind quadratic residues and quadratic non-residues mod p. The main methods we used are the properties of the Legendre's symbol mod p, and the estimate for character sums. As application, we solve two open problems proposed by Zhiwei Sun.
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收藏
页数：8
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