Abstract
Let q, h, a, b be integers with q > 0. The classical and the homogeneous Dedekind sums are defined by
respectively, where
The Knopp identities for the classical and the homogeneous Dedekind sum were the following:
where σ(n) =Σ d|n d.
In this paper generalized homogeneous Hardy sums and Cochrane-Hardy sums are defined, and their arithmetic properties are studied. Generalized Knopp identities for homogeneous Hardy sums and Cochrane-Hardy sums are given.
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Supported by the National Natural Science Foundation of China under Grant No. 10901128, the Specialized Research Fund for the Doctoral Program of Higher Education of China under Grant No. 20090201120061, and the Fundamental Research Funds for the Central University.
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Liu, H., Gao, J. Generalized Knopp identities for homogeneous Hardy sums and Cochrane-Hardy sums. Czech Math J 62, 1147–1159 (2012). https://doi.org/10.1007/s10587-012-0069-7
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DOI: https://doi.org/10.1007/s10587-012-0069-7