Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A pair correlation problem, and counting lattice points with the zeta
  function   The pair correlation is a localized statistic for sequences in the unit
interval. Pseudo-random behavior with respect to this statistic is called
Poissonian behavior. The metric theory of pair correlations of sequences of the
form $(a_n \alpha)_{n \geq 1}$ has been pioneered by Rudnick, Sarnak and
Zaharescu. Here $\alpha$ is a real parameter, and $(a_n)_{n \geq 1}$ is an
integer sequence, often of arithmetic origin. Recently, a general framework was
developed which gives criteria for Poissonian pair correlation of such
sequences for almost every real number $\alpha$, in terms of the additive
energy of the integer sequence $(a_n)_{n \geq 1}$. In the present paper we
develop a similar framework for the case when $(a_n)_{n \geq 1}$ is a sequence
of reals rather than integers, thereby pursuing a line of research which was
recently initiated by Rudnick and Technau. As an application of our method, we
prove that for every real number $\theta>1$, the sequence $(n^\theta \alpha)_{n
\geq 1}$ has Poissonian pair correlation for almost all $\alpha \in
\mathbb{R}$.

28
The categories of this paper are: alg-geom
23
The categories of this paper are: solv-int
22
The categories of this paper are: chao-dyn
29
The categories of this paper are: funct-an
1
The categories of this paper are: cs
32
The categories of this paper are: atom-ph
6
The categories of this paper are: astro-ph
0
The categories of this paper are: hep-ph
34
The categories of this paper are: chem-ph
35
The categories of this paper are: mtrl-th
4
The categories of this paper are: cond-mat
26
The categories of this paper are: bayes-an
36
The categories of this paper are: cmp-lg
16
The categories of this paper are: stat
20
The categories of this paper are: acc-phys
27
The categories of this paper are: comp-gas