Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Mobius and Liouville functions of order $k$   Let $F$ be a number field, $k$ a positive integer. In this paper, we define
the Mobius and Liouville functions of order $k$ in $F$. We give a formula about
the partial sums of them by using elementary number theory and complex
analysis. Moreover, we also consider the number of $k$-free ideals of the
integer ring of $F$.

31
The categories of this paper are: ao-sci
7
The categories of this paper are: hep-th
26
The categories of this paper are: bayes-an
5
The categories of this paper are: gr-qc
14
The categories of this paper are: math-ph
23
The categories of this paper are: solv-int
4
The categories of this paper are: cond-mat
21
The categories of this paper are: adap-org
27
The categories of this paper are: comp-gas
36
The categories of this paper are: cmp-lg
35
The categories of this paper are: mtrl-th
25
The categories of this paper are: patt-sol
9
The categories of this paper are: nlin
0
The categories of this paper are: hep-ph
3
The categories of this paper are: physics
8
The categories of this paper are: hep-ex