Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A continuous transition from $\mathcal{E}$-sets to $R$-sets and beyond   The well-known $\mathcal{E}$-sets introduced by Hayman in 1960 are
collections of Euclidean discs in the complex plane with the following
property: The set of angles $\theta$ for which the ray $\arg(z)=\theta$ meets
infinitely many discs in a given $\mathcal{E}$-set has linear measure zero. An
important special case of an $\mathcal{E}$-set is known as the $R$-set. These
sets appear in numerous papers in the theories of complex differential and
functional equations. This paper offers a continuous transition from
$\mathcal{E}$-sets to $R$-sets, and then to much thinner sets. In addition to
rays, plane curves that originate from the zero distribution theory of
exponential polynomials will be considered. It turns out that almost every such
curve meets at most finitely many discs in the collection in question.
Analogous discussions are provided in the case of the unit disc $\mathbb{D}$,
where the curves tend to the boundary $\partial\mathbb{D}$ tangentially or
non-tangentially. Finally, these findings will be used for improving well-known
estimates for logarithmic derivatives, logarithmic differences and logarithmic
$q$-differences of meromorphic functions, as well as for improving standard
results on exceptional sets.

0
The categories of this paper are: hep-ph
33
The categories of this paper are: plasm-ph
16
The categories of this paper are: stat
8
The categories of this paper are: hep-ex
20
The categories of this paper are: acc-phys
7
The categories of this paper are: hep-th
25
The categories of this paper are: patt-sol
11
The categories of this paper are: hep-lat
18
The categories of this paper are: econ
12
The categories of this paper are: nucl-th
27
The categories of this paper are: comp-gas
26
The categories of this paper are: bayes-an
17
The categories of this paper are: q-fin
4
The categories of this paper are: cond-mat
29
The categories of this paper are: funct-an
10
The categories of this paper are: q-bio