Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Some refined results on mixed Littlewood conjecture for pseudo-absolute
  values   In this paper, we study the mixed Littlewood conjecture with pseudo-absolute
values. For any pseudo absolute value sequence $\mathcal{D}$, we obtain the
sharp criterion such that for almost every $\alpha$ the inequality
\begin{equation*}
  |n|_{\mathcal{D}}|n\alpha -p|\leq \psi(n) \end{equation*} has infinitely many
coprime solutions $(n,p)\in\N\times \Z$ for a certain one-parameter family of
$\psi$. Also under minor condition on pseudo absolute value sequences
$\mathcal{D}_1$,$\mathcal{D}_2,\cdots, \mathcal{D}_k$, we obtain a sharp
criterion on general sequence $\psi(n)$ such that for almost every $\alpha$ the
inequality \begin{equation*}
  |n|_{\mathcal{D}_1}|n|_{\mathcal{D}_2}\cdots
|n|_{\mathcal{D}_k}|n\alpha-p|\leq \psi(n) \end{equation*} has infinitely many
coprime solutions $(n,p)\in\N\times \Z$.

5
The categories of this paper are: gr-qc
3
The categories of this paper are: physics
23
The categories of this paper are: solv-int
18
The categories of this paper are: econ
6
The categories of this paper are: astro-ph
26
The categories of this paper are: bayes-an
34
The categories of this paper are: chem-ph
10
The categories of this paper are: q-bio
32
The categories of this paper are: atom-ph
29
The categories of this paper are: funct-an
24
The categories of this paper are: dg-ga
16
The categories of this paper are: stat
12
The categories of this paper are: nucl-th
1
The categories of this paper are: cs
0
The categories of this paper are: hep-ph
27
The categories of this paper are: comp-gas