Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Rational approximation and arithmetic progressions   A reasonably complete theory of the approximation of an irrational by
rational fractions whose numerators and denominators lie in prescribed
arithmetic progressions is developed in this paper. Results are both, on the
one hand, from a metrical and a non-metrical point of view and, on the other
hand, from an asymptotic and also a uniform point of view. The principal
novelty is a Khintchine type theorem for uniform approximation in this context.
Some applications of this theory are also discussed.

1
The categories of this paper are: cs
8
The categories of this paper are: hep-ex
11
The categories of this paper are: hep-lat
10
The categories of this paper are: q-bio
4
The categories of this paper are: cond-mat
35
The categories of this paper are: mtrl-th
23
The categories of this paper are: solv-int
14
The categories of this paper are: math-ph
19
The categories of this paper are: eess
16
The categories of this paper are: stat
15
The categories of this paper are: nucl-ex
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The categories of this paper are: chao-dyn
36
The categories of this paper are: cmp-lg
6
The categories of this paper are: astro-ph
37
The categories of this paper are: supr-con
24
The categories of this paper are: dg-ga