On a generalization of arithmetic functions and the Ramanujan sums

Yusuke Fujisawa

Published 2012-12-09, updated 2014-04-27Version 2

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.