Quadratic residues and non-residues in arithmetic progression

JOURNAL OF NUMBER THEORY

卷:133

Article

Wright, Steve

关键词: Quadratic residue;    Quadratic non-residue;    Arithmetic progression;    Asymptotic approximation;    Weil sum;   

DOI  :  10.1016/j.jnt.2013.01.004

来源: Elsevier

【 摘 要 】

Let S be an infinite set of nonempty, finite subsets of the positive integers. If p is an odd prime, let c(p) denote the cardinality of the set {S is an element of S: S subset of {1, ... , p - 1} and S is a set of quadratic residues (respectively, non-residues) of p}. When S is constructed in various ways from the set of all arithmetic progressions of positive integers, we determine the sharp asymptotic behavior of c(p) as p -> +infinity. Generalizations and variations of this are also established, and some problems connected with these results that are worthy of further study are discussed. (c) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free