Mittelwert der Eulerschen φ-Funktion und des Quadrates der Dirichletschen Teilerfunktion in algebraischen Zahlkörpern

Abstract

LetK be an algebraic number field, and for every integer γ∈K let φ(γ) andd(γ), respectively, denote the number of relatively prime residue classes and the number of divisors of the principal ideal (γ). Asymptotic equalities are proved for the sums Σφ(γ) and Σd ²(γ), where γ runs through certain finite sets of integers ofK.