Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Irrationality exponent and rational approximations with prescribed
  growth   Let $\xi$ be a real irrational number. We are interested in sequences of
linear forms in 1 and $\xi$, with integer coefficients, which tend to 0. Does
such a sequence exist such that the linear forms are small (with given rate of
decrease) and the coefficients have some given rate of growth? If these rates
are essentially geometric, a necessary condition for such a sequence to exist
is that the linear forms are not too small, a condition which can be expressed
precisely using the irrationality exponent of $\xi$. We prove that this
condition is actually sufficient, even for arbitrary rates of growth and
decrease. We also make some remarks and ask some questions about multivariate
generalizations connected to Fischler-Zudilin's new proof of Nesterenko's
linear independence criterion.

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The categories of this paper are: gr-qc
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The categories of this paper are: nucl-th
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The categories of this paper are: physics
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The categories of this paper are: cs
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The categories of this paper are: supr-con
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The categories of this paper are: stat
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The categories of this paper are: astro-ph
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The categories of this paper are: eess
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The categories of this paper are: chao-dyn
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The categories of this paper are: econ
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The categories of this paper are: funct-an
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The categories of this paper are: hep-lat
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The categories of this paper are: math-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: quant-ph
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The categories of this paper are: chem-ph