Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On $\mathcal I(<q)$- and $\mathcal I(\leq q)$-convergence of arithmetic
  functions   Let $\mathbb N$ be the set of positive integers, and denote by
$\lambda(A)=\inf\{t>0:\sum_{a\in A} a^{-t}<\infty\}$ the convergence exponent
of $A\subset\mathbb N$. For $0<q\le 1$, $0\le q\le 1$, respectively, the
admissible ideals $\mathcal I(<q)$, $\mathcal I(\leq q)$ of all subsets
$A\subset \mathbb N$ with $\lambda(A)<q$, $\lambda(A)\le q$, respectively,
satisfy $\mathcal I(<q)\subsetneq\mathcal I_c^{(q)}\subsetneq \mathcal I(\leq
q)$, where $\mathcal I_c^{(q)}=\{A\subset\mathbb N: \sum_{a\in
A}a^{-q}<\infty\}$. In this note we sharpen the results of Bal\'az, Gogola and
Visnyai from [2], and of others papers, concerning characterizations of
$\mathcal I_c^{(q)}$-convergence of various arithmetic functions in terms of
$q$. This is achieved by utilizing $\mathcal I(<q)$- and $\mathcal I(\leq
q)$-convergence, for which new methods and criteria are developed.

15
The categories of this paper are: nucl-ex
9
The categories of this paper are: nlin
23
The categories of this paper are: solv-int
6
The categories of this paper are: astro-ph
1
The categories of this paper are: cs
30
The categories of this paper are: q-alg
4
The categories of this paper are: cond-mat
36
The categories of this paper are: cmp-lg
19
The categories of this paper are: eess
32
The categories of this paper are: atom-ph
0
The categories of this paper are: hep-ph
20
The categories of this paper are: acc-phys
22
The categories of this paper are: chao-dyn
21
The categories of this paper are: adap-org
16
The categories of this paper are: stat
29
The categories of this paper are: funct-an