Visual properties of generalized Kloosterman sums

被引：3

作者：

Burkhardt, Paula ^{[2
]}

Chan, Alice Zhuo-Yu ^{[1
]}

Currier, Gabriel ^{[2
]}

Garcia, Stephan Ramon ^{[2
]}

Luca, Florian ^{[3
]}

Suh, Hong ^{[2
]}

机构：

[1] Univ Calif San Diego, Dept Math, La Jolla, CA 92093 USA

[2] Pomona Coll, Dept Math, Claremont, CA 91711 USA

[3] Univ Witwatersrand, Sch Math, ZA-2050 Johannesburg, South Africa

来源：

JOURNAL OF NUMBER THEORY | 2016年 / 160卷

基金：

美国国家科学基金会;

关键词：

Kloosterman sum; Gauss sum; Salie sum; Supercharacter; Hypocycloid; Uniform distribution; Equidistribution; Lucas number; Lucas prime; GRAPHIC NATURE; SUPERCHARACTERS;

D O I：

10.1016/j.jnt.2015.08.019

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

For a positive integer m and a subgroup Lambda of the unit group (Z/mZ)(x), the corresponding generalized Kloosterrnan sum is the function K(a, b, m, Lambda) = Sigma(u is an element of Lambda) e(au+bu(-1)/m) for a, b is an element of Z/mZ. Unlike classical Kloosterman sums, which are real valued, generalized Kloosterman sums display a surprising array of visual features when their values are plotted in the complex plane. In a variety of instances, we identify the precise number-theoretic conditions that give rise to particular phenomena. (C) 2015 Elsevier Inc. All rights reserved.

引用

页码：237 / 253

页数：17

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