三次Gauss和及二项指数和的混合均值
On the Hybrid Power Mean of Three-th Gauss Sums and Two-term Exponential Sums
我们用三角和的性质研究一类三次Gauss和与两项指数和混合均值的计算问题,并给出一个精确的计算公式.
The main purpose of this paper is using the analytic method and the properties of classical Gauss sums and 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.
三次Gauss和 / 二项指数和 / 混合均值 / 解析方法 / 计算公式 {{custom_keyword}} /
three-th Gauss sums / two-term exponential sums / hybrid power mean / analytic method / computational formula {{custom_keyword}} /
[1] Apostol T. M., Introduction to Analytic Number Theory, Springer-Verlag, New York, 1976.
[2] Chen L., Hu J., A linear Recurrence Formula Involving Cubic Gauss Sums and Kloosterman Sums, Acta Mathematica Sinica, Chinese Series, 2018, 61(1): 67–72.
[3] Cochrane T., Pinner C., Using Stepanov's method for exponential sums involving rational functions, Journal of Number Theory, 2006, 116: 270–292.
[4] Cochrane T., Zheng Z., Bounds for certain exponential sums, Asian J. Math., 2000, 4: 757–774.
[5] Weil A., On some exponential sums, Proceedings of the National Academy of Sciences of the United States of America, 1948, 34: 204–207.
[6] Zhang H., Zhang W., The fourth power mean of two-term exponential sums and its application, Mathematical Reports, 2017, 19: 75–83.
[7] Zhang W., Han D., On the sixth power mean of the two-term exponential sums, Journal of Number Theory, 2014, 136: 403–413.
[8] Zhang W., Hu J., The number of solutions of the diagonal cubic congruence equation mod p, Mathematical Reports, 2018, 20: 60–66.
[9] Zhang W., Liu H., On the general Gauss sums and their fourth power mean, Osaka Journal of Mathematics, 2005, 42: 189–199.
[10] Zhang W., Shen M., A note on the fourth power mean of the generalized Kloosterman sums, Journal of Number Theory, 2017, 174: 419–426.
[11] Zhang W., On the number of the solutions of one kind congruence equation modp, Journal of Northwest University, Natural Science Edition, 2016, 46: 3153–316.
国家自然科学基金资助项目(11771351)
/
〈 | 〉 |