Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Pair Correlation of the Fractional Parts of $\alpha n^\theta$   Fix $\alpha,\theta >0$, and consider the sequence $(\alpha n^{\theta} \mod
1)_{n\ge 1}$. Since the seminal work of Rudnick--Sarnak (1998), and due to the
Berry--Tabor conjecture in quantum chaos, the fine-scale properties of these
dilated mononomial sequences have been intensively studied. In this paper we
show that for $\theta \le 1/3$, and $\alpha>0$, the pair correlation function
is Poissonian. While (for a given $\theta \neq 1$) this strong
pseudo-randomness property has been proven for almost all values of $\alpha$,
there are next-to-no instances where this has been proven for explicit
$\alpha$. Our result holds for all $\alpha>0$ and relies solely on classical
Fourier analytic techniques. This addresses (in the sharpest possible way) a
problem posed by Aistleitner--El-Baz--Munsch (2021).

26
The categories of this paper are: bayes-an
3
The categories of this paper are: physics
13
The categories of this paper are: quant-ph
12
The categories of this paper are: nucl-th
29
The categories of this paper are: funct-an
31
The categories of this paper are: ao-sci
24
The categories of this paper are: dg-ga
36
The categories of this paper are: cmp-lg
4
The categories of this paper are: cond-mat
8
The categories of this paper are: hep-ex
32
The categories of this paper are: atom-ph
10
The categories of this paper are: q-bio
6
The categories of this paper are: astro-ph
7
The categories of this paper are: hep-th
35
The categories of this paper are: mtrl-th
11
The categories of this paper are: hep-lat