[For the entire collection see Zbl 0674.00008.]
For an ideal \({\mathfrak a}\neq (0)\) in the ring of algebraic integers in a quadratic number field \(K={\mathbb{Q}}(\sqrt{D})\) let N(\({\mathfrak a})\) be the norm of \({\mathfrak a}\) and \(\Phi\) (\({\mathfrak a})\) the number of those residue classes which are prime to \({\mathfrak a}\). Generalizing results for Euler’s \(\phi\)-function the author establishes asymptotic formulas for \(\sum \Phi ({\mathfrak a})\), \(\sum \Phi ({\mathfrak a})N({\mathfrak a})^{-1}\), \(\sum \Phi ({\mathfrak a})^{-1}\) and \(\sum N({\mathfrak a})\Phi ({\mathfrak a})^{-1}\) where each summation is extended over all ideals \({\mathfrak a}\) with N(\({\mathfrak a})\leq x\). Further he gives asymptotics with error terms for the mean- values of the corresponding remainder terms.