Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On sequences of rational interpolants of the exponential function with
  unbounded interpolation points   We consider sequences of rational interpolants $r_n(z)$ of degree $n$ to the
exponential function $e^z$ associated to a triangular scheme of complex points
$\{z_{j}^{(2n)}\}_{j=0}^{2n}$, $n>0$, such that, for all $n$,
$|z_{j}^{(2n)}|\leq cn^{1-\alpha}$, $j=0,...,2n$, with $0<\alpha\leq 1$ and
$c>0$. We prove the local uniform convergence of $r_{n}(z)$ to $e^{z}$ in the
complex plane, as $n$ tends to infinity, and show that the limit distributions
of the conveniently scaled zeros and poles of $r_{n}$ are identical to the
corresponding distributions of the classical Pad\'e approximants. This extends
previous results obtained in the case of bounded (or growing like $\log n$)
interpolation points. To derive our results, we use the Deift-Zhou steepest
descent method for Riemann-Hilbert problems. For interpolation points of order
$n$, satisfying $|z_{j}^{(2n)}|\leq cn$, $c>0$, the above results are false if
$c$ is large, e.g. $c\geq 2\pi$. In this connection, we display numerical
experiments showing how the distributions of zeros and poles of the
interpolants may be modified when considering different configurations of
interpolation points with modulus of order $n$.

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The categories of this paper are: gr-qc
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The categories of this paper are: cmp-lg
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The categories of this paper are: econ
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The categories of this paper are: solv-int
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The categories of this paper are: supr-con
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The categories of this paper are: patt-sol
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The categories of this paper are: chem-ph
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The categories of this paper are: nlin
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The categories of this paper are: plasm-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: math-ph
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The categories of this paper are: q-fin
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The categories of this paper are: bayes-an
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: stat