Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On a distribution function of a probability measure involving a
  permutation   In [3], we have introduced a probability measure to study the power and
exponential sums for a certain coding system. The distribution function of the
probability measure gives explicit formulas for the power and exponential sums.
  [3,Theorem 4] states that the higher order derivatives of the distribution
function with respect to a certain parameter are expressed by a generalization
of the Takagi function. In [3], we only gave the sketch of the proof of Theorem
4, because the complete proof is very long. The purpose of this paper is to
give the complete proof of [3,Theorem 4].

5
The categories of this paper are: gr-qc
31
The categories of this paper are: ao-sci
34
The categories of this paper are: chem-ph
12
The categories of this paper are: nucl-th
1
The categories of this paper are: cs
9
The categories of this paper are: nlin
25
The categories of this paper are: patt-sol
3
The categories of this paper are: physics
13
The categories of this paper are: quant-ph
20
The categories of this paper are: acc-phys
10
The categories of this paper are: q-bio
33
The categories of this paper are: plasm-ph
14
The categories of this paper are: math-ph
23
The categories of this paper are: solv-int
27
The categories of this paper are: comp-gas
0
The categories of this paper are: hep-ph