Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quantitative non-divergence and lower bounds for points with algebraic
  coordinates near manifolds   Point counting estimates are a key stepping stone to various results in
metric Diophantine approximation. In this paper we use the quantitative
non-divergence estimates originally developed by Kleinbock and Margulis to
improve lower bounds by Bernik, G\"{o}tze et al. for the number of points with
algebraic conjugate coordinates close to a given manifold. In the process, we
also improve on a Khinchin-Groshev-type theorem for a problem of constrained
approximation by polynomials.

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The categories of this paper are: dg-ga
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The categories of this paper are: comp-gas
0
The categories of this paper are: hep-ph
22
The categories of this paper are: chao-dyn
31
The categories of this paper are: ao-sci
30
The categories of this paper are: q-alg
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The categories of this paper are: nucl-ex
3
The categories of this paper are: physics
33
The categories of this paper are: plasm-ph
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The categories of this paper are: q-fin
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The categories of this paper are: adap-org
8
The categories of this paper are: hep-ex
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The categories of this paper are: acc-phys
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The categories of this paper are: funct-an
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The categories of this paper are: math-ph
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The categories of this paper are: econ