经典高斯和及它们的一些递推性质

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经典高斯和及它们的一些递推性质徐小玲¹, 张佳凡²1. 延安大学西安创新学院西安 710100;
2. 西北大学数学学院西安 710127 A Certain Classical Gauss Sums and Some of Their Recursive Properties Xiao Ling XU¹, Jia Fan ZHANG²1. School of Data Science and Engineering, Xi'an Innovation College of Yan'an University, Xi'an 710100, P. R. China;
2. School of Mathematics, Northwest University, Xi'an, Shaanxi 710127, P. R. China

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摘要本文利用解析方法及经典高斯和的性质研究了某些特殊对称高斯和的计算问题，并给出了一些新的恒等式及其二阶线性递推公式.

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收稿日期: 2020-05-08

MR (2010):

O156.4

基金资助:国家自然科学基金项目（11771351）；陕西省教育厅2019年度专项科学研究计划（19JK0978）

作者简介: 徐小玲,E-mail:yadxxxl@163.com;张佳凡,E-mail:zhangjiafan@stumail.nwu.edu.cn

引用本文:

徐小玲, 张佳凡. 经典高斯和及它们的一些递推性质[J]. 数学学报, 2021, 64(3): 479-484. Xiao Ling XU, Jia Fan ZHANG. A Certain Classical Gauss Sums and Some of Their Recursive Properties. Acta Mathematica Sinica, Chinese Series, 2021, 64(3): 479-484.

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[1] Apostol Tom M., Introduction to Analytic Number Theory, Springer-Verlag, New York, 1976.
[2] Bai H., Hu J. Y., On the classical Gauss sum and the recursive properties, Advances in Difference Equations, 2018, 2018:387.
[3] Berndt B. C., Evans R. J., Sums of Gauss, Jacobi, and Jacobsthal, Journal of Number Theory, 1979, 11:349-389.
[4] Berndt B. C., Evans R. J., The determination of Gauss sums, Bulletin of the American Mathematical Society, 1981, 5:107-128.
[5] Chen L., On the classical Gauss sums and their some properties, Symmetry, 2018, 10:625.
[6] Chen L., Hu J. Y., A linear Recurrence Formula Involving Cubic Gauss Sums and Kloosterman Sums, Acta Mathematica Sinica, Chinese Series, 2018, 61:67-72.
[7] Chen Z. Y., Zhang W. P., On the fourth-order linear recurrence formula related to classical Gauss sums, Open Mathematics, 2017, 15:1251-1255.
[8] Chowla S., Cowles J., Cowles M., On the number of zeros of diagonal cubic forms, Journal of Number Theory, 1977, 9:502-506.
[9] Ireland K., Rosen M., A Classical Introduction to Modern Number Theory, Springer-Verlag, New York, 1982.
[10] Kim T., Dolgy D. V., Kim D. S., Representing sums of finite products of Chebyshev polynomials of the second kind and Fibonacci polynomials in terms of Chebyshev polynomials, Advanced Studies in Contemporary Mathematics, 2018, 28:321-336.
[11] Kim T., Kim D. S., Dolgy D. V., et al., Sums of finite products of Chebyshev polynomials of the third and fourth kinds, Advances in Difference Equations, 2018, 2018:283.
[12] Kim T., Kim D. S., Dolgy D. V., et al., Representation by several orthogonal polynomials for sums of finite products of Chebyshev polynomials of the first, third and fourth kinds, Advances in Difference Equations, 2019, 2019:110.
[13] Kim T., Kim D. S., Jang L. C., et al., Representing by several orthogonal polynomials for sums of finite products of Chebyshev polynomials of the first kind and Lucas polynomials, Advances in Difference Equations, 2019, 2019:162.
[14] Pan C. D., Pan C. B., Goldbach Conjecture (in Chinese), Science Press, Beijing, 1992.
[15] Ren G. L., He D. D., Zhang T. P., On general partial Gaussian sums, J. Inequal. Appl., 2016, 2016:295.
[16] Shen S. M., Zhang W. P., On the quartic Gauss sums and their recurrence property, Advances in Difference Equations, 2017, 2017:43.
[17] Wang T. T., Chen G. H., A note on the classical Gauss sums, Mathematics, 2018, 6:313.
[18] Zhang W. P., Hu J. Y., The number of solutions of the diagonal cubic congruence equation mod p, Mathematical Reports, 2018, 20:73-80.

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