Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Integer points on spheres and their orthogonal grids   The set of primitive vectors on large spheres in the euclidean space of
dimension d>2 equidistribute when projected on the unit sphere. We consider
here a refinement of this problem concerning the direction of the vector
together with the shape of the lattice in its orthogonal complement. Using
unipotent dynamics we obtained the desired equidistribution result in dimension
d>5 and in dimension d=4,5 under a mild congruence condition on the square of
the radius. The case of d=3 is considered in a separate paper.

25
The categories of this paper are: patt-sol
34
The categories of this paper are: chem-ph
11
The categories of this paper are: hep-lat
13
The categories of this paper are: quant-ph
37
The categories of this paper are: supr-con
21
The categories of this paper are: adap-org
23
The categories of this paper are: solv-int
10
The categories of this paper are: q-bio
3
The categories of this paper are: physics
20
The categories of this paper are: acc-phys
31
The categories of this paper are: ao-sci
33
The categories of this paper are: plasm-ph
22
The categories of this paper are: chao-dyn
0
The categories of this paper are: hep-ph
1
The categories of this paper are: cs
15
The categories of this paper are: nucl-ex