Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sharp form for improved Moser-Trudinger inequality   We prove that the improved Moser-Trudinger inequality with optimal
coefficient $\alpha =1/2$ holds for all functions on $S^2$ with zero moments.

1
The categories of this paper are: cs
20
The categories of this paper are: acc-phys
11
The categories of this paper are: hep-lat
24
The categories of this paper are: dg-ga
22
The categories of this paper are: chao-dyn
36
The categories of this paper are: cmp-lg
3
The categories of this paper are: physics
0
The categories of this paper are: hep-ph
30
The categories of this paper are: q-alg
34
The categories of this paper are: chem-ph
5
The categories of this paper are: gr-qc
12
The categories of this paper are: nucl-th
9
The categories of this paper are: nlin
7
The categories of this paper are: hep-th
28
The categories of this paper are: alg-geom
14
The categories of this paper are: math-ph