Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Approximation of complex algebraic numbers by algebraic numbers of
  bounded degree   We investigate how well complex algebraic numbers can be approximated by
algebraic numbers of degree at most n. We also investigate how well complex
algebraic numbers can be approximated by algebraic integers of degree at most
n+1. It follows from our investigations that for every positive integer n there
are complex algebraic numbers of degree larger than n that are better
approximable by algebraic numbers of degree at most n than almost all complex
numbers. As it turns out, these numbers are more badly approximable by
algebraic integers of degree at most n+1 than almost all complex numbers.

11
The categories of this paper are: hep-lat
24
The categories of this paper are: dg-ga
5
The categories of this paper are: gr-qc
25
The categories of this paper are: patt-sol
22
The categories of this paper are: chao-dyn
14
The categories of this paper are: math-ph
28
The categories of this paper are: alg-geom
12
The categories of this paper are: nucl-th
15
The categories of this paper are: nucl-ex
9
The categories of this paper are: nlin
32
The categories of this paper are: atom-ph
34
The categories of this paper are: chem-ph
27
The categories of this paper are: comp-gas
8
The categories of this paper are: hep-ex
4
The categories of this paper are: cond-mat
13
The categories of this paper are: quant-ph