Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Somewhat smooth numbers in short intervals   We use exponent pairs to establish the existence of many $x^a$-smooth numbers
in short intervals $[x-x^b,x]$, when $a>1/2$. In particular, $b=1-a-a(1-a)^3$
is admissible. Assuming the exponent-pairs conjecture, one can take
$b=(1-a)/2+\epsilon$. As an application, we show that $[x-x^{0.4872},x]$
contains many practical numbers when $x$ is large.

24
The categories of this paper are: dg-ga
11
The categories of this paper are: hep-lat
26
The categories of this paper are: bayes-an
21
The categories of this paper are: adap-org
34
The categories of this paper are: chem-ph
5
The categories of this paper are: gr-qc
18
The categories of this paper are: econ
22
The categories of this paper are: chao-dyn
7
The categories of this paper are: hep-th
37
The categories of this paper are: supr-con
1
The categories of this paper are: cs
10
The categories of this paper are: q-bio
31
The categories of this paper are: ao-sci
28
The categories of this paper are: alg-geom
15
The categories of this paper are: nucl-ex
32
The categories of this paper are: atom-ph