Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On univalent polynomials with critical points on the unit circle   Brannan showed that a normalized univalent polynomial of the form $P(z)=z+a_2
z^2+\ldots + a_{n-1}z^{n-1}+\frac{z^n}{n}$ is starlike if and only if
$a_2=\ldots=a_{n-1}=0$. We give a new and simple proof of his result, showing
further that it is also equivalent to the membership of $P$ in the
Noshiro-Warschawski class of univalent functions whose derivative has positive
real part in the disk. Both proofs are based on the Fej\'er lemma for
trigonometric polynomials with positive real part.

16
The categories of this paper are: stat
12
The categories of this paper are: nucl-th
15
The categories of this paper are: nucl-ex
25
The categories of this paper are: patt-sol
13
The categories of this paper are: quant-ph
17
The categories of this paper are: q-fin
27
The categories of this paper are: comp-gas
36
The categories of this paper are: cmp-lg
37
The categories of this paper are: supr-con
8
The categories of this paper are: hep-ex
19
The categories of this paper are: eess
7
The categories of this paper are: hep-th
30
The categories of this paper are: q-alg
3
The categories of this paper are: physics
26
The categories of this paper are: bayes-an
14
The categories of this paper are: math-ph