On a generalization of arithmetic functions and the Ramanujan sums
  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. 
Yusuke Fujisawa
math.NT