Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Congruences in fractional partition functions   The coefficients of the generating function $(q;q)^\alpha_\infty$ produce
$p_\alpha(n)$ for $\alpha \in \mathbb{Q}$. In particular, when $\alpha = -1$,
the partition function is obtained. Recently, Chan and Wang identified and
proved congruences of the form $p_{\frac{a}{b}}(\ell n + c)\equiv 0
\pmod{\ell}$ where $\ell$ is a prime such that $\ell \mid a -db$ for $d \in
\{4, 6, 8, 10, 14, 26\}$. Expanding upon their work, we use the representation
of powers of the Dedekind-eta functions in linear sums of Hecke eigenforms and
their lacunarity to raise the power of the modulus to higher powers of $\ell$.
In addition, we generate congruences for when $d=2$ employing Hecke algebra.

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The categories of this paper are: physics
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The categories of this paper are: astro-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: hep-lat
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The categories of this paper are: plasm-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: stat
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The categories of this paper are: atom-ph
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The categories of this paper are: eess
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The categories of this paper are: math-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-bio
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The categories of this paper are: ao-sci
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The categories of this paper are: patt-sol
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-th