Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Distributions of Distances and Volumes of Balls in Homogeneous Lens
  Spaces   Lens spaces are a family of manifolds that have been a source of many
interesting phenomena in topology and differential geometry. Their concrete
construction, as quotients of odd-dimensional spheres by a free linear action
of a finite cyclic group, allows a deeper analysis of their structure. In this
paper, we consider the problem of moments for the distance function between
randomly selected pairs of points on homogeneous three-dimensional lens spaces.
We give a derivation of a recursion relation for the moments, a formula for the
$k$th moment, and a formula for the moment generating function, as well as an
explicit formula for the volume of balls of all radii in these lens spaces.

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The categories of this paper are: bayes-an
4
The categories of this paper are: cond-mat
14
The categories of this paper are: math-ph
18
The categories of this paper are: econ
33
The categories of this paper are: plasm-ph
28
The categories of this paper are: alg-geom
13
The categories of this paper are: quant-ph
12
The categories of this paper are: nucl-th
32
The categories of this paper are: atom-ph
3
The categories of this paper are: physics
37
The categories of this paper are: supr-con
22
The categories of this paper are: chao-dyn
10
The categories of this paper are: q-bio
31
The categories of this paper are: ao-sci
7
The categories of this paper are: hep-th
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The categories of this paper are: adap-org