Gauss和与广义Kloosterman和的几个新的恒等式

李江华, 刘燕妮

数学学报 ›› 2013, Vol. 56 ›› Issue (3) : 413-418.

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数学学报 ›› 2013, Vol. 56 ›› Issue (3) : 413-418. DOI: 10.12386/A2013sxxb0041
论文

Gauss和与广义Kloosterman和的几个新的恒等式

    李江华1, 刘燕妮2
作者信息 +

Some New Identities Involving Gauss Sums and General Kloosterman Sums

    Jiang Hua LI1, Yan Ni LIU2
Author information +
文章历史 +

摘要

主要应用Gauss和的性质和解析方法来研究Gauss和与广义Kloosterman 和之间的关系, 并且给出了几个有趣的恒等式.

Abstract

The main purpose of this paper is using the properties of Gauss sums and the analytic method to study the the hybrid mean value problem involving between the Gauss sums and the general Kloosterman sums, and to give several interesting identities of it.

关键词

Gauss和 / 广义Kloosterman和 / 恒等式 / 解析方法

Key words

Gauss sums / the general Kloosterman sums / identity / analytic method

引用本文

导出引用
李江华, 刘燕妮. Gauss和与广义Kloosterman和的几个新的恒等式. 数学学报, 2013, 56(3): 413-418 https://doi.org/10.12386/A2013sxxb0041
Jiang Hua LI, Yan Ni LIU. Some New Identities Involving Gauss Sums and General Kloosterman Sums. Acta Mathematica Sinica, Chinese Series, 2013, 56(3): 413-418 https://doi.org/10.12386/A2013sxxb0041

参考文献

[1] Apostol Tom M., Introduction to Analytic Number Theory, Springer-Verlag, New York, 1976.

[2] Davenport H., Multiplicative Number Theory, Markham, 1967.

[3] Montgomery H. L., Topics in Multiplicative Number Theory, Lecture Notes in Math. 227, Springer-Verlag, Heidelberg, 1971.

[4] Hua L. K., Introduction to Number Theory, Science Press, Beijing, 1979.

[5] Pan C. D., Pan C. B., Goldbach Conjecture, Science Press, Beijing, 1992.

[6] Zhang W. P., On the fourth power mean of the general Kloosterman sums, Indian J. Pure and Applied Mathematics, 2004, 35: 237-242.

[7] Chowla S., On Kloosterman's sum, Norkse Vid. Selbsk. Fak. Frondheim., 1967, 40: 70-72.

[8] Malyshev A. V., A generalization of Kloosterman sums and their estimates (in Russian), Vestnik Leningrad University, 1960, 15: 59-75.

基金

陕西省自然科学基金资助项目(2012K06-43)及陕西省教育厅基金资助项目(12JK0874)

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