Abstract
Let \(\textit{K}\) be a cubic number field. In this paper, we study the Ramanujan sums \(c_{\mathcal {J}}(\mathcal {I})\), where \(\mathcal {I}\) and \(\mathcal {J}\) are integral ideals in \(\mathcal {O}_\textit{K}\). The asymptotic behaviour of sums of \(c_{\mathcal {J}}(\mathcal {I})\) over both \(\mathcal {I}\) and \(\mathcal {J}\) is investigated.
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Acknowledgements
This work is supported in part by the National Natural Science Foundation of China (Grant No. 11971476, 11771252).
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Ma, J., Sun, H. & Zhai, W. The average size of Ramanujan sums over cubic number fields. Period Math Hung 87, 215–231 (2023). https://doi.org/10.1007/s10998-022-00507-0
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DOI: https://doi.org/10.1007/s10998-022-00507-0