Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the number of representations of integers as differences between
  Piatetski-Shapiro numbers   For $\alpha>1$, set $\beta=1/(\alpha-1)$. We show that, for every
$1<\alpha<(\sqrt{21}+4)/5\approx1.717$, the number of pairs $(m,n)$ of positive
integers with $d=\lfloor{n^\alpha}\rfloor - \lfloor{m^\alpha}\rfloor$ is equal
to $\beta\alpha^{-\beta}\zeta(\beta)d^{\beta-1} + o(d^{\beta-1})$ as
$d\to\infty$, where $\zeta$ denotes the Riemann zeta function. We use this
result to derive an asymptotic formula for the number of triplets $(l,m,n)$ of
positive integers such that $l<x$ and $\lfloor{l^\alpha}\rfloor +
\lfloor{m^\alpha}\rfloor = \lfloor{n^\alpha}\rfloor$.

9
The categories of this paper are: nlin
35
The categories of this paper are: mtrl-th
16
The categories of this paper are: stat
5
The categories of this paper are: gr-qc
28
The categories of this paper are: alg-geom
15
The categories of this paper are: nucl-ex
24
The categories of this paper are: dg-ga
4
The categories of this paper are: cond-mat
18
The categories of this paper are: econ
10
The categories of this paper are: q-bio
0
The categories of this paper are: hep-ph
23
The categories of this paper are: solv-int
3
The categories of this paper are: physics
7
The categories of this paper are: hep-th
33
The categories of this paper are: plasm-ph
30
The categories of this paper are: q-alg