The least k-th power non-residue

被引：8

作者：

Trevino, Enrique ^{[1
]}

机构：

[1] Lake Forest Coll, Dept Math & Comp Sci, Lake Forest, IL 60045 USA

来源：

JOURNAL OF NUMBER THEORY | 2015年 / 149卷

关键词：

Character sums; Explicit estimates; Burgess inequality;

D O I：

10.1016/j.jnt.2014.10.019

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let p be a prime number and let k >= 2 be a divisor of p - 1. Norton proved that the least k-th power non-residue mod p is at most 3.9p(1/4) logp unless k = 2 and p equivalent to 3 (mod 4), in which case the bound is 4.7p(1/4) logp. By improving the upper bound in the Burgess inequality via a combinatorial idea, and by using some computing power, we improve the upper bounds to 0.9p(1/4) logp and 1.1p(1/4) logp, respectively. (C) 2014 Elsevier Inc. All rights reserved.

引用

页码：201 / 224

页数：24