Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Generators of the ring of weakly holomorphic modular functions for
  $\Gamma_1(N)$   For a positive integer $N$ divisible by $4,5,6,7$ or $9$, let
$\mathcal{O}_{1,N}(\mathbb{Q})$ be the ring of weakly holomorphic modular
functions for the congruence subgroup $\Gamma_1(N)$ with rational Fourier
coefficients. We present explicit generators of the ring
$\mathcal{O}_{1,N}(\mathbb{Q})$ over $\mathbb{Q}$ by making use of modular
units which have infinite product expansions.

16
The categories of this paper are: stat
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The categories of this paper are: comp-gas
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The categories of this paper are: acc-phys
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The categories of this paper are: q-fin
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The categories of this paper are: dg-ga
7
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: ao-sci
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The categories of this paper are: nucl-ex
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The categories of this paper are: quant-ph
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The categories of this paper are: eess
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The categories of this paper are: hep-lat
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The categories of this paper are: mtrl-th
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The categories of this paper are: cmp-lg
10
The categories of this paper are: q-bio
9
The categories of this paper are: nlin