Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On transference principle and Nesterenko's linear independence criterion   We consider the problem of simultaneous approximation of real numbers
$\theta_1, \ldots,\theta_n$ with rationals and the dual problem of
approximating zero with the values of the linear form
$x_0+\theta_1x_1+\ldots+\theta_nx_n$ at integer points. In this setting we
analyse two transference inequalities obtained by Schmidt and Summerer. We
present a rather simple geometric observation, which proves their result. We
also derive several corollaries previously unknown. Particularly, we show that,
together with the transference inequalities for uniform exponents, Schmidt and
Summerer's inequalities imply the inequalities by Bugeaud and Laurent and "one
half" of the inequalities by Marnat and Moshchevitin. Besides that, we show
that our main construction provides a rather simple proof of Nesterenko's
linear independence criterion.

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The categories of this paper are: math-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-th
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The categories of this paper are: astro-ph
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The categories of this paper are: ao-sci
4
The categories of this paper are: cond-mat
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The categories of this paper are: dg-ga
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The categories of this paper are: stat
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The categories of this paper are: mtrl-th
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The categories of this paper are: plasm-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: alg-geom
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The categories of this paper are: solv-int
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The categories of this paper are: q-fin
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The categories of this paper are: quant-ph
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The categories of this paper are: adap-org