Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Duffin-Schaeffer conjecture   Let $\psi:\mathbb{N}\to\mathbb{R}_{\ge0}$ be an arbitrary function from the
positive integers to the non-negative reals. Consider the set $\mathcal{A}$ of
real numbers $\alpha$ for which there are infinitely many reduced fractions
$a/q$ such that $|\alpha-a/q|\le \psi(q)/q$. If $\sum_{q=1}^\infty
\psi(q)\phi(q)/q=\infty$, we show that $\mathcal{A}$ has full Lebesgue measure.
This answers a question of Duffin and Schaeffer. As a corollary, we also
establish a conjecture due to Catlin regarding non-reduced solutions to the
inequality $|\alpha - a/q|\le \psi(q)/q$, giving a refinement of Khinchin's
Theorem.

17
The categories of this paper are: q-fin
26
The categories of this paper are: bayes-an
8
The categories of this paper are: hep-ex
16
The categories of this paper are: stat
34
The categories of this paper are: chem-ph
14
The categories of this paper are: math-ph
21
The categories of this paper are: adap-org
32
The categories of this paper are: atom-ph
24
The categories of this paper are: dg-ga
9
The categories of this paper are: nlin
6
The categories of this paper are: astro-ph
7
The categories of this paper are: hep-th
5
The categories of this paper are: gr-qc
10
The categories of this paper are: q-bio
33
The categories of this paper are: plasm-ph
20
The categories of this paper are: acc-phys