Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Extremal quasimodular forms of lower depth with integral Fourier
  coefficients   We show that, based on Grabner's recent results on modular differential
equations satisfied by quasimodular forms, there exist only finitely many
normalized extremal quasimodular forms of depth $r$ that have all Fourier
coefficients integral for each of $r=1,2,3,4$, and partly classifies them,
where the classification is complete for $r=2,3,4$; in fact, we show that there
exists no normalized extremal quasimodular forms of depth $4$ with all Fourier
coefficients integral. Our result disproves a conjecture by Pellarin.

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The categories of this paper are: hep-th
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The categories of this paper are: math-ph
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The categories of this paper are: nlin
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The categories of this paper are: solv-int
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The categories of this paper are: chem-ph
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The categories of this paper are: q-bio
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The categories of this paper are: hep-ph
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The categories of this paper are: atom-ph
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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: patt-sol
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The categories of this paper are: comp-gas
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The categories of this paper are: q-alg
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The categories of this paper are: alg-geom
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The categories of this paper are: gr-qc
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The categories of this paper are: mtrl-th