| 广义Dedekind和与Hardy和 |
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| 引用本文： | 刘华宁,张文鹏. 广义Dedekind和与Hardy和[J]. 数学学报, 2006, 49(5): 999-100. DOI: cnki:ISSN:0583-1431.0.2006-05-005 |
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| 作者姓名： | 刘华宁 张文鹏 |
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| 作者单位： | 西北大学数学系,西安710069 |
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| 基金项目： | 国家自然科学基金资助项目（10271093,60472068） |
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| 摘 要： | 本文给出了广义Dedekind和与Hardy和的定义,研究了广义Dedekind和的算术性质,并把Hardy和表示成广义Dedekind和的形式．提出了广义Subrahmanyam等式和Knopp定理,并给出了证明．
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| 关 键 词： | Dedekind和 Subrahmanyam等式 Knopp定理 |
| 文章编号： | 0583-1431（2006）05-0999-10 |
| 收稿时间： | 2005-03-14 |
| 修稿时间： | 2005-03-142005-05-30 |
Generalized Dedekind Sums and Hardy Sums |
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| Hua Ning LIU, Wen Peng ZHANG. Generalized Dedekind Sums and Hardy Sums[J]. Acta Mathematica Sinica, 2006, 49(5): 999-100. DOI: cnki:ISSN:0583-1431.0.2006-05-005 |
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| Authors: | Hua Ning LIU Wen Peng ZHANG |
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| Affiliation: | Hua Ning LIU Wen Peng ZHANG Department of Mathematics, Northwest University, Xi'an 710069, P. R. China |
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| Abstract: | In this paper, the generalized Dedekind sums and Hardy sums are defined. The arithmetic properties of the generalized Dedekind sums are studied, and the generalized Hardy sums are expressed in terms of the generalized Dedekind sums. Finally, the generalized Subrahmanyam's identities and Knopp's theorems are given and proved. |
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| Keywords: | Dedekind sums Subrahmanyam's identity Knopp's theorem |
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