In this paper we study Ramanujan sums $c_{\bf m}(\bf n)$, where $ {\bf m}$ and ${\bf n}$ are integral ideals in an arbitrary quadratic number field. We give some new results about the asymptotic behavior of sums of $c_{\bf m}(\bf n)$ over both $ {\bf m}$ and $ {\bf n}$.
Analytic continuation of multiple zeta-functions and the asymptotic behavior at non-positive integers
The Average Size of Ramanujan Sums over Cubic Number Fields
$E_8$ and the average size of the 3-Selmer group of the Jacobian of a pointed genus-2 curve
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