Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Initial Log-Concavity in Power of Infinite Series Close to $(1 -
  z)^{-1}$   Using the analytic method of Odlyzko and Richmond, we show that if $f(z) =
\sum_n a_nz^n$ is an infinite series with $a_n \geq 1$ and $a_0 + \cdots + a_n
= O(n + 1)$ for all $n$, then a super-polynomially long initial segment of
$f^k(z)$ is log-concave. Furthermore, if $a_0 + \cdots + a_n = C(n + 1) + O((n
+ 1)^{\alpha})$ for constants $C > 1$ and $\alpha < 1$, we show that an
exponentially long initial segment of $f^k(z)$ is log-concave. This resolves a
conjecture of the author and Letong Hong in arXiv:2008.10069, and resolves a
conjecture of Heim and Neuhauser in arXiv:1810.02226 that the Nekrasov-Okounkov
polynomials $Q_n(z)$ are unimodal for sufficiently large $n$.

24
The categories of this paper are: dg-ga
0
The categories of this paper are: hep-ph
29
The categories of this paper are: funct-an
12
The categories of this paper are: nucl-th
31
The categories of this paper are: ao-sci
25
The categories of this paper are: patt-sol
20
The categories of this paper are: acc-phys
22
The categories of this paper are: chao-dyn
13
The categories of this paper are: quant-ph
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The categories of this paper are: stat
9
The categories of this paper are: nlin
8
The categories of this paper are: hep-ex
21
The categories of this paper are: adap-org
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The categories of this paper are: bayes-an
35
The categories of this paper are: mtrl-th
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The categories of this paper are: eess