两个不同Gauss和的混合均值

刘宝利, 申诗萌

数学学报 ›› 2019, Vol. 62 ›› Issue (2) : 255-260.

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数学学报 ›› 2019, Vol. 62 ›› Issue (2) : 255-260. DOI: 10.12386/A2019sxxb0023
论文

两个不同Gauss和的混合均值

    刘宝利1, 申诗萌2
作者信息 +

On the Hybrid Power Mean of Two Different Gauss Sums

    Bao Li LIU1, Shi Meng SHEN2
Author information +
文章历史 +

摘要

本文利用解析方法以及三角和的性质研究两个不同Gauss和的混合均值的计算问题,并给出一个精确的计算公式. 作为我们结果的应用,得到了关于模p的一类对角同余方程解的个数的计算公式,其中p是一个奇素数.

Abstract

The main purpose of this paper is using the analytic method and the properties of trigonometric sums to study the computational problem of one kind hybrid power mean of two different Gauss sums, and give an exact computational formula for it. As an application of our result, we give an exact formula for the number of solutions of one kind diagonal congruence equation mod p, where p is an odd prime.

关键词

k-次Gauss和 / 混合均值 / 解析方法 / 计算公式

Key words

The k-th Gauss sums / hybrid power mean / analytic method / computational formula

引用本文

导出引用
刘宝利, 申诗萌. 两个不同Gauss和的混合均值. 数学学报, 2019, 62(2): 255-260 https://doi.org/10.12386/A2019sxxb0023
Bao Li LIU, Shi Meng SHEN. On the Hybrid Power Mean of Two Different Gauss Sums. Acta Mathematica Sinica, Chinese Series, 2019, 62(2): 255-260 https://doi.org/10.12386/A2019sxxb0023

参考文献

[1] Apostol T. M., Introduction to Analytic Number Theory, Springer-Verlag, New York, 1976.
[2] Weil A., On some exponential sums, Proc. Nat. Acad. Sci. U.S.A., 1948, 34(5): 204–207.
[3] Zhang W. P., Han D., On the sixth power mean of the two-term exponential sums, Journal of Number Theory, 136(2014): 403–413.
[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 W. P., Liu H. N., On the general Gauss sums and their fourth power mean, Osaka Journal of Mathematics, 2005, 42: 189–199.
[6] Cochrane T., Zheng Z., Bounds for certain exponential sums, Asian J. Math., 2000, 4: 757–774.
[7] Zhang W. P., On the fourth power mean of the general Kloosterman sums, Journal of Number Theory, 2016, 169: 315–326.
[8] Zhang W. P., Shen S. M., A note on the fourth power mean of the generalized Kloosterman sums, Journal of Number Theory, 2017, 174: 419–426.
[9] Zhang H., Zhang W. P., The fourth power mean of two-term exponential sums and its application, Mathematical Reports, 2017, 19: 75–83.
[10] Zhang W. P., Hu J. Y., The number of solutions of the diagonal cubic congruence equation mod p, Mathematical Reports, 2018, 20: 60–66.

基金

国家自然科学基金资助项目(11771351);海南省自然科学基金资助项目(118MS041)

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