Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Inhomogeneous Diophantine approximation for generic homogeneous
  functions   The present paper is a sequel to arXiv:1910.02067 in which results of that
paper are generalized so that they hold in the setting of inhomogeneous
Diophantine approximation. Given any integers $n \geq 2$ and $\ell \geq 1$, any
$\pmb \xi = (\xi_1, \dots, \xi_\ell) \in \mathbb{R}^\ell$, and any homogeneous
function $f = (f_1, \dots , f_\ell): \mathbb{R}^n \to \mathbb{R}^\ell$ that
satisfies a certain nonsingularity assumption, we obtain a biconditional
criterion on the approximating function $\psi = (\psi_1, \dots, \psi_\ell):
\mathbb{R}_{\geq 0} \to (\mathbb{R}_{>0})^\ell$ for a generic element in the
$G$-orbit of $f$ to be (respectively, not to be) $\psi$-approximable at $\pmb
\xi$: that is, for there to exist infinitely many (respectively, only finitely
many) $\mathbf{v} \in \mathbb{Z}^n$ such that $|\xi_j - (f_j \circ
g)(\mathbf{v})| \leq \psi_j(\|\mathbf{v}\|)$ for each $j \in \{1, \dots,
\ell\}$. In this setting, we also obtain a sufficient condition for uniform
approximation. We also consider some examples of $f$ that do not satisfy our
nonsingularity assumptions and prove similar results for these examples. Here,
$G$ can be any closed subgroup of $\mathrm{ASL}_n(\mathbb{R})$ (such as
$\mathrm{ASL}_n(\mathbb{R})$ itself or $\mathrm{SL}_n(\mathbb{R})$) that
satisfies certain axioms introduced by the authors in the aforementioned
previous paper.

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The categories of this paper are: hep-ex
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The categories of this paper are: nucl-ex
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The categories of this paper are: econ
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The categories of this paper are: patt-sol
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The categories of this paper are: cmp-lg
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The categories of this paper are: q-alg
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The categories of this paper are: math-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: chao-dyn
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The categories of this paper are: alg-geom
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The categories of this paper are: nlin
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The categories of this paper are: ao-sci
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The categories of this paper are: q-bio
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The categories of this paper are: adap-org
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The categories of this paper are: physics
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The categories of this paper are: astro-ph