Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Fractional parts of powers of real algebraic numbers   Let $\alpha$ be a real number greater than $1$. We establish an effective
lower bound for the distance between an integral power of $\alpha$ and its
nearest integer.

18
The categories of this paper are: econ
6
The categories of this paper are: astro-ph
35
The categories of this paper are: mtrl-th
13
The categories of this paper are: quant-ph
26
The categories of this paper are: bayes-an
21
The categories of this paper are: adap-org
1
The categories of this paper are: cs
32
The categories of this paper are: atom-ph
5
The categories of this paper are: gr-qc
4
The categories of this paper are: cond-mat
37
The categories of this paper are: supr-con
20
The categories of this paper are: acc-phys
28
The categories of this paper are: alg-geom
10
The categories of this paper are: q-bio
0
The categories of this paper are: hep-ph
22
The categories of this paper are: chao-dyn