广义Kloosterman和及它的四次均值
The generalized Kloosterman sums and their fourth power mean
崔俊峰 1王丽2
作者信息
- 1. 陇南师范高等专科学校数学系,甘肃陇南 742500
- 2. 西北大学数学学院数论及其应用研究中心,陕西西安 710127
- 折叠
摘要
为了研究对任意素数模p的一类广义Kloosterman和的四次均值,利用初等与解析方法、Gauss和以及三角和的转换性质引入了当素数p≡1mod4时该均值的计算问题,并将该类均值转化为特征和的简易形式.从计算结果上对均值的估计具有充分性,从计算方法上对广义Kloost-erman 和各种形式的四次均值研究具有重要的参考价值.此外,这也为指数和均值计算问题提供了一种新的转化思路与方法,必将对有关问题的进一步探索起到推动作用.
Abstract
In order to study the fourth power mean of a kind of generalized Kloosterman sums for modulo p of arbitrary prime numbers.By using elementary and analytic methods,properties of Gauss sums and trigonometric sums,we introduce the computational problem of the power mean when the prime number is p≡1mod4,and give a simplified form of the character sums.Suffi-cient to estimate the mean value from the calculation results,it has important reference value for the study of generalized Kloosterman and various forms of fourth power mean from the calcula-tion methods.In addition,it provides a new idea and method for the calculation of power mean of exponential sums,which promotes the further exploration of related problems.
关键词
广义Kloosterman和/四次均值/解析方法/简化形式Key words
generalized Kloosterman sums/the fourth power mean/analytic method/simplified form引用本文复制引用
出版年
2024
国家科技期刊平台
NSTL
万方数据