二项指数和四次均值的一个注记

王啸

数学学报 ›› 2019, Vol. 62 ›› Issue (2) : 261-268.

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PDF(361 KB)
数学学报 ›› 2019, Vol. 62 ›› Issue (2) : 261-268. DOI: 10.12386/A2019sxxb0024
论文

二项指数和四次均值的一个注记

    王啸
作者信息 +

A Note on the Fourth Power Mean of the Two-term Exponential Sums

    Xiao WANG
Author information +
文章历史 +

摘要

本文利用初等方法以及三角和的性质研究一类二项指数和四次均值的计算问题,并给出一个精确的计算公式.

Abstract

The main purpose of this paper is using the elementary methods and the properties of the trigonometric sums to study the computational problem of one kind fourth power mean of the two-term exponential sums, and give a precise computational formula for it.

关键词

二项指数和 / 四次均值 / 初等方法 / 计算公式

Key words

The two-term exponential sums / fourth power mean / elementary method / computational formula

引用本文

导出引用
王啸. 二项指数和四次均值的一个注记. 数学学报, 2019, 62(2): 261-268 https://doi.org/10.12386/A2019sxxb0024
Xiao WANG. A Note on the Fourth Power Mean of the Two-term Exponential Sums. Acta Mathematica Sinica, Chinese Series, 2019, 62(2): 261-268 https://doi.org/10.12386/A2019sxxb0024

参考文献

[1] Apostol T. M., Introduction to Analytic Number Theory, Springer-Verlag, New York, 1976.
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[3] Cochrane T., Exponential sums modulo prime powers, Acta Arithmetica, 2002, 101: 131–149.
[4] Cochrane T., Pinner C., Using Stepanov's method for exponential sums involving rational functions, Journal of Number Theory, 2006, 116: 270–292.
[5] Zhang H., Zhang W. P., The fourth power mean of two-term exponential sums and its application, Mathematical Reports, 2017, 19: 75–83.
[6] Zhang H., Zhang W. P., On the fourth power mean of the two-term exponential sums, The Scientific World Journal, 2014, 2014, Article ID: 724840.
[7] Zhang T. P., On mixed two-term exponential sums, Journal of the Korean Mathematical Society, 2010, 47: 1107–1122.
[8] Zhang W. P., On the number of the solutions of one kind congruence equation mod p, Journal of Northwest University (Natural Science Edition), 2016, 46: 313–316.
[9] Zhang W. P., Han D., On the sixth power mean of the two-term exponential sums, Journal of Number Theory, 2014, 136: 403–413.
[10] Zhang W. P., Hu J. Y., The number of solutions of the diagonal cubic congruence equation mod p, Mathematical Reports, 2018, 20: 73–80.

基金

国家自然科学基金资助项目(11771351)

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