On some arithmetical functions and the number of pure number fields
First, we define the Möbius and Liouville functions of order $k$ over a number field $F$ for a positive integer $k$. We give formulas for their partial sums. Moreover, we consider the number of $k$-free ideals of the integer ring of $F$.
Next, we investigate the number of pure number fields. In the previous paper, we considered lower and upper bounds of that number. However, the estimates were too coarse. One of the purposes of this paper is to improve the upper bound.