Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Weierstrass Sigma Function Coefficients Divisibility Hypothesis   We consider the coefficients in the series expansion at zero of the
Weierstrass sigma function \[ \sigma(z) = z \sum_{i, j \geqslant 0} {a_{i,j}
\over (4 i + 6 j + 1)!} \left({g_2 z^4 \over 2}\right)^i \left(2 g_3
z^6\right)^j. \] We have $a_{i,j} \in \mathbb{Z}$. We present the divisibility
Hypothesis for the integers $a_{i,j}$ \begin{align*} \nu_2(a_{i,j}) &=
\nu_2((4i + 6j + 1)!) - \nu_2(i!) - \nu_2(j!) - 3 i - 4 j, & \nu_3(a_{i,j}) &=
\nu_3((4i + 6j + 1)!) - \nu_3(i!) - \nu_3(j!) - i - j. \end{align*} If this
conjecture holds, then $\sigma(z)$ is a Hurwitz series over the ring
$\mathbb{Z}[{g_2 \over 2}, 6 g_3]$.

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The categories of this paper are: hep-th
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The categories of this paper are: econ
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The categories of this paper are: q-bio
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-ex
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The categories of this paper are: mtrl-th
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The categories of this paper are: cond-mat
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The categories of this paper are: funct-an
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The categories of this paper are: nlin
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The categories of this paper are: acc-phys
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The categories of this paper are: nucl-ex
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The categories of this paper are: chao-dyn
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The categories of this paper are: solv-int
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The categories of this paper are: plasm-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: cs