
一类四项指数和的四次均值
On the Fourth Power Mean of One Kind Four-term Exponential Sums
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.
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.
四项指数和 / 四次均值 / 恒等式 {{custom_keyword}} /
The four-term exponential sums / the fourth power mean / identity {{custom_keyword}} /
[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.
国家自然科学基金资助项目(11771351)
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