Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Anharmonic Oscillators with Infinitely Many Real Eigenvalues and
  PT-Symmetry   We study the eigenvalue problem $-u"+V(z)u=\lambda u$ in the complex plane
with the boundary condition that $u(z)$ decays to zero as $z$ tends to infinity
along the two rays $\arg z=-\frac{\pi}{2} \pm \frac{2\pi}{m+2}$, where
$V(z)=-(iz)^m-P(iz)$ for complex-valued polynomials $P$ of degree at most
$m-1\geq 2$. We provide an asymptotic formula for eigenvalues and a necessary
and sufficient condition for the anharmonic oscillator to have infinitely many
real eigenvalues.

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The categories of this paper are: ao-sci
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The categories of this paper are: nucl-ex
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The categories of this paper are: stat
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The categories of this paper are: econ
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The categories of this paper are: hep-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: nucl-th
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The categories of this paper are: gr-qc
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The categories of this paper are: eess
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The categories of this paper are: q-fin
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The categories of this paper are: mtrl-th
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The categories of this paper are: hep-th
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The categories of this paper are: nlin
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The categories of this paper are: q-bio
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The categories of this paper are: hep-lat
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The categories of this paper are: chao-dyn