Abstract
In this paper, we study Ramanujan sums \(c_{\mathcal {J}}({\mathcal {I}})\), where \({\mathcal {I}}\) and \({\mathcal {J}}\) are integral ideals in an arbitrary quadratic number field. In particular, the asymptotic behaviour of sums of \(c_{\mathcal {J}}({\mathcal {I}})\) over both \({\mathcal {I}}\) and \({\mathcal {J}}\) is investigated.
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The author deeply thanks the referee for many valuable suggestions, which significantly improved the quality of this paper.
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This work is supported by the National Natural Science Foundation of China (Grant No. 11971476).
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Zhai, W. The average size of Ramanujan sums over quadratic number fields. Ramanujan J 56, 953–969 (2021). https://doi.org/10.1007/s11139-020-00363-x
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DOI: https://doi.org/10.1007/s11139-020-00363-x