广义四次Gauss和的四次均值

杜先存, 李小雪

数学学报 ›› 2018, Vol. 61 ›› Issue (4) : 541-548.

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PDF(373 KB)
数学学报 ›› 2018, Vol. 61 ›› Issue (4) : 541-548. DOI: 10.12386/A2018sxxb0048
论文

广义四次Gauss和的四次均值

    杜先存1, 李小雪2
作者信息 +

On the Fourth Power Mean of the Generalized Quartic Gauss Sums

    Xian Cun DU1, Xiao Xue LI2
Author information +
文章历史 +

摘要

本文利用解析方法以及经典Gauss和的性质,研究了模p为奇素数时广义四次Gauss和的四次均值的计算问题,并根据p≡3或1 mod 4,得到了该四次均值的一个精确计算公式和渐近公式.

Abstract

The main purpose of this paper is using the analytic method and the properties of the classical Gauss sums to study the computational problem of the fourth power mean of the generalized quartic Gauss sums mod p, an odd prime, and give an exact computational formula and asymptotic formula for it according to p ≡ 3 or 1 mod 4.

关键词

广义四次Gauss和 / 四次均值 / 解析方法 / 恒等式 / 渐近公式

Key words

generalized quartic Gauss sums / fourth power mean / analytic method / identity / asymptotic formula

引用本文

导出引用
杜先存, 李小雪. 广义四次Gauss和的四次均值. 数学学报, 2018, 61(4): 541-548 https://doi.org/10.12386/A2018sxxb0048
Xian Cun DU, Xiao Xue LI. On the Fourth Power Mean of the Generalized Quartic Gauss Sums. Acta Mathematica Sinica, Chinese Series, 2018, 61(4): 541-548 https://doi.org/10.12386/A2018sxxb0048

参考文献

[1] Apostol T. M., Introduction to Analytic Number Theory, Springer-Verlag, New York, 1976.
[2] Cochrane T., Zheng Z., Bounds for certain exponential sums, Asian J. Math., 2000, 4(4):757-774.
[3] Liu H. Y., On the fourth power mean of the general fourth Gauss sum, J. Sys. Sci. & Math. Scis., 2004, 24(3):289-295.
[4] Weil A., On some exponential sums, Proc. Nat. Acad. Sci. U.S.A., 1948, 34(5):204-207.
[5] Zhang W. P., Han D., On the sixth power mean of the two-term exponential sums, J. Number Theory, 2014, 136:403-413.
[6] Zhang W. P., Li H. L., Elementary Number Theory, Shaanxi Normal University General Publishing House, Xi'an, 2013.
[7] Zhang W. P., Liu H. N., On the general Gauss sums and their fourth power mean, Osaka J. Math., 2005, 42(1):189-199.

基金

国家自然科学基金资助项目(11771351)

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