Consecutive Quadratic Residues and Primitive Roots in the Sequences Formed by Twice-differentiable Functions

被引:3
作者
Jing, Mengyao [1 ]
Liu, Huaning [1 ]
机构
[1] Northwest Univ, Res Ctr Number Theory & Its Applicat, Sch Math, Xian 710127, Shaanxi, Peoples R China
来源
TAIWANESE JOURNAL OF MATHEMATICS | 2022年 / 26卷 / 03期
基金
中国国家自然科学基金;
关键词
quadratic residue; primitive root; twice-differentiable function; character sum; NONRESIDUES; SUMS;
D O I
10.11650/tjm/211206
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
In this paper we bound character sums of the shape Sigma(n <= N) chi(1)(left perpendicularf(n)right perpendicular)chi(2)(left perpendicularf(n + l)right perpendicular), where chi(1) and chi(2) are non-principal multiplicative characters modulo a prime p, f(x) is a real-valued, twice-differentiable function satisfying a certain condition on f ''(x), and l is a positive integer. As an immediate application, we obtain some distribution properties of consecutive quadratic residues and consecutive primitive roots in Piatetski-Shapiro sequences left perpendicularn(c)right perpendicular with c is an element of (1, 4/3).
引用
收藏
页码:445 / 461
页数:17
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