Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the growth and zeros of polynomials attached to arithmetic functions   In this paper we investigate growth properties and the zero distribution of
polynomials attached to arithmetic functions $g$ and $h$, where $g$ is
normalized, of moderate growth, and $0<h(n) \leq h(n+1)$. We put
$P_0^{g,h}(x)=1$ and \begin{equation*} P_n^{g,h}(x) := \frac{x}{h(n)}
\sum_{k=1}^{n} g(k) \, P_{n-k}^{g,h}(x). \end{equation*} As an application we
obtain the best known result on the domain of the non-vanishing of the Fourier
coefficients of powers of the Dedekind $\eta$-function. Here, $g$ is the sum of
divisors and $h$ the identity function. Kostant's result on the representation
of simple complex Lie algebras and Han's results on the Nekrasov--Okounkov hook
length formula are extended. The polynomials are related to reciprocals of
Eisenstein series, Klein's $j$-invariant, and Chebyshev polynomials of the
second kind.

29
The categories of this paper are: funct-an
31
The categories of this paper are: ao-sci
20
The categories of this paper are: acc-phys
22
The categories of this paper are: chao-dyn
26
The categories of this paper are: bayes-an
11
The categories of this paper are: hep-lat
0
The categories of this paper are: hep-ph
37
The categories of this paper are: supr-con
13
The categories of this paper are: quant-ph
12
The categories of this paper are: nucl-th
4
The categories of this paper are: cond-mat
5
The categories of this paper are: gr-qc
1
The categories of this paper are: cs
18
The categories of this paper are: econ
6
The categories of this paper are: astro-ph
24
The categories of this paper are: dg-ga