The average size of Ramanujan sums over quadratic number fields |
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Authors: | Werner Georg Nowak |
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Institution: | 1. Department of Integrative Biology, Institute of Mathematics, BOKUWien, 1180, Vienna, Austria
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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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