广义Dedekind和与Hardy和

刘华宁;张文鹏;

数学学报 ›› 2006, Vol. 49 ›› Issue (5) : 999-100.

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PDF(351 KB)
数学学报 ›› 2006, Vol. 49 ›› Issue (5) : 999-100. DOI: 10.12386/A2006sxxb0123
论文

广义Dedekind和与Hardy和

    刘华宁;张文鹏;
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Generalized Dedekind Sums and Hardy Sums

    Hua Ning LIU; Wen Peng ZHANG
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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.

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.

关键词

Subrahmanyam等式 / Knopp定理 / Dedekind和

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刘华宁;张文鹏;. 广义Dedekind和与Hardy和. 数学学报, 2006, 49(5): 999-100 https://doi.org/10.12386/A2006sxxb0123
Hua Ning LIU; Wen Peng ZHANG. Generalized Dedekind Sums and Hardy Sums. Acta Mathematica Sinica, Chinese Series, 2006, 49(5): 999-100 https://doi.org/10.12386/A2006sxxb0123
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