On a generalization of arithmetic functions and the Ramanujan sums

Abstract

Let $K$ be a number field. This paper considers arithmetic functions over $K$, that are, complex valued functions on the set of nonzero integral ideals in $K$. Firstly we generalize some basic results on arithmetic functions. Next we define the generalized Ramanujan sums over $K$ and show some properties.

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Cited by in corpus (1)

• On partial sums of the Möbius and Liouville functions for number fields