Abstract
This article is concerned with Ramanujan sums \({c_{\mathcal{I}_1}(\mathcal{I}),}\) where \({\mathcal{I},\mathcal{I}_1}\) are integral ideals in an arbitrary quadratic number field \({\mathbb{Q}(\sqrt{d}).}\) In particular, the asymptotic behavior of sums of \({c_{\mathcal{I}_1}(\mathcal{I}),}\) over both \({\mathcal{I}}\) and \({c_{\mathcal{I}_1}(\mathcal{I}),}\) is investigated.
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The author gratefully acknowledges support from the Austrian Science Fund (FWF) under project Nr. P20847-N18.
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Nowak, W.G. The average size of Ramanujan sums over quadratic number fields. Arch. Math. 99, 433–442 (2012). https://doi.org/10.1007/s00013-012-0442-7
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DOI: https://doi.org/10.1007/s00013-012-0442-7