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| 摘要: |
| 本文进一步深入研究了三项指数和四次均值的计算问题.运用指数和的相关性质并结合求解同余方程组的方法与技巧，利用两种不同的方法获得了两个精确的均值计算公式，揭示了三项指数和的计算与同余方程组解的个数之间的本质联系，推广了已有的结果. |
| 关键词: 三项指数和 四次均值 转换公式 同余方程组 |
| DOI： |
| 分类号:O156.4 |
| 基金项目:国家自然科学基金（NSFC61502156）；海军工程大学自然科学基金（HGDQNSQJJ15001）；湖北省自然科学基金（2014CFB189）；湖北工业大学博士启动基金（BSQD13051）. |
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| RESEARCHING THE RELATION BETWEEN THE THREE-TERM EXPONENTIAL SUMS AND THE SYSTEM OF THE CONGRUENCE EQUATIONS |
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AI Xiao-chuan,CHEN Hua,ZHANG Si-lan
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| Abstract: |
| In this paper, the computation problem of the fourth power mean of the three-term exponential sums is further studied. By using the properties of exponential sums and various techniques and methods of solving the system of congruence equations, two explicit formulas of mean value are given throughout two difierent methods. Moreover, the essential relation between the fourth moment and the system of congruence equations is discovered. |
| Key words: three-term exponential sum fourth power mean transform formula the system of congruence equations |
