| A Generalization on the Difference Between an Integer and Its Inverse Modulo Q |
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| 作者姓名： | Tian Ping ZHANG Wen Peng ZHANG |
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| 作者单位： | [1]Department of Mathematics, Northwest University, Xi＇an 710069, P. R. China [2]College of Mathematics and Information Science, Shannxi Normal University, Xi＇an 710062, P. R. China |
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| 基金项目： | This work is supported by the N.S.F.（10271093,60472068） and P.N.S.F of P.R.China |
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| 摘 要： | The main purpose of this paper is to use the properties of the Gauss sums, primitive characters and the mean value of Dirichlet L-functions to study the hybrid mean value of the error term E（n, l, c, q） and the hyper-Kloosterman sums K（h,n＋1,q）, the asymptotic property of the mean square value ∑^p c=1 E^2（n, 1, c, p）, and give two interesting mean value formulae.
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| 关 键 词： | 平均数 整数 相反娄数 高斯和 |
| 文章编号： | 10.1007/s10114-007-0942-8 |
| 收稿时间： | 2004-02-09 |
| 修稿时间： | 2004-10-11 |
A generalization on the difference between an integer and its inverse modulo <Emphasis Type="Italic">Q</Emphasis> |
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| Tian Ping ZHANG Wen Peng ZHANG.A Generalization on the Difference Between an Integer and Its Inverse Modulo Q[J].Acta Mathematica Sinica,2008,24(2):215-222. |
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| Authors: | Tian Ping Zhang Wen Peng Zhang |
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| Institution: | (1) Department of Mathematics, Northwest University, Xi’an, 710069, P. R. China;(2) College of Mathematics and Information Science, Shannxi Normal University, Xi’an, 710062, P. R. China;(3) Department of Mathematics, Northwest University, Xi’an, 710069, P. R. China |
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| Abstract: | The main purpose of this paper is to use the properties of the Gauss sums, primitive characters and the mean value of Dirichlet
L-functions to study the hybrid mean value of the error term E(n, 1, c, q) and the hyper-Kloosterman sums K(h, n+1, q), the asymptotic property of the mean square value Σ
c=1
p
E
2(n, 1, c, p), and give two interesting mean value formulae.
This work is supported by the N.S.F. (10271093, 60472068) and P.N.S.F of P. R. China |
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| Keywords: | generalization mean value hyper-Kloosterman sums |
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