一类四项指数和的四次均值

刘馨予, 陈卓钰

数学学报 ›› 2020, Vol. 63 ›› Issue (3) : 261-270.

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数学学报 ›› 2020, Vol. 63 ›› Issue (3) : 261-270. DOI: 10.12386/A2020sxxb0022
论文

一类四项指数和的四次均值

    刘馨予, 陈卓钰
作者信息 +

On the Fourth Power Mean of One Kind Four-term Exponential Sums

    Xin Yu LIU, Zhuo Yu CHEN
Author information +
文章历史 +

摘要

本文利用三角和的性质以及同余方程解的个数研究了一类四项指数和的四次均值的计算问题,并给出两个精确的计算公式.

Abstract

The main purpose of this paper is using the properties of the trigonometric sums and the number of the congruence equation to study the computational problem of the one kind fourth power mean involving the four-term exponential sums, and give two interesting computational formulae for it.

关键词

四项指数和 / 四次均值 / 恒等式

Key words

The four-term exponential sums / the fourth power mean / identity

引用本文

导出引用
刘馨予, 陈卓钰. 一类四项指数和的四次均值. 数学学报, 2020, 63(3): 261-270 https://doi.org/10.12386/A2020sxxb0022
Xin Yu LIU, Zhuo Yu CHEN. On the Fourth Power Mean of One Kind Four-term Exponential Sums. Acta Mathematica Sinica, Chinese Series, 2020, 63(3): 261-270 https://doi.org/10.12386/A2020sxxb0022

参考文献

[1] Apostol T. M., Introduction to Analytic Number Theory, Springer-Verlag, New York, 1976.
[2] Birch B. J., How the number of points of an elliptic curve over a fixed prime field varies, Journal of London Math. Soc., 1968, 43:57-60.
[3] Chen H., Zhang T. P., On the fourth power mean of the analogous general Kloosterman sums, Journal of Number Theory, 2016, 160:326-333.
[4] Cochrane T., Exponential sums modulo prime powers, Acta Arithmetica, 2002, 101:131-149.
[5] Du X. Y., The hybrid power mean of two-term exponential sums and character sums, Acta Mathematica Sinica, Chinese Series, 2016, 59:309-316.
[9] Duke W., Iwaniec H., A relation between cubic exponential and Kloosterman sums, Contemporary Mathematics, 1993, 143:255-258.
[7] Han D., A Hybrid mean value involving two-term exponential sums and polynomial character sums, Czechoslovak Mathematical Journal, 2014, 6:53-62.
[8] Wang X. Y., Li X. X., One kind sixth power mean of the three-term exponential sums, Open Mathematics, 2017, 1:705-710.
[9] Weil A., On some exponential sums, Proc. Nat. Acad. Sci. U.S.A., 1948, 34:203-210.
[10] Xu Z. F., Zhang T. P., Zhang W. P., On the mean value of the two-term exponential sums with Dirichlet characters, Journal of Number Theory, 2007, 123:352-362.
[11] Zhang T. P., On mixed two-term exponential sums, Journal of the Korean Mathematical Society, 2010, 47:1107-1122.
[13] Zhang W. P., Han D., On the sixth power mean of the two-term exponential sums, Journal of Number Theory, 2014, 136:403-413.
[13] Zhang H., Zhang W. P., The fourth power mean of two-term exponential sums and its application, Mathematical Reports, 2017, 19:75-81.

基金

国家自然科学基金资助项目(11771351)

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