Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Zeros of certain combinations of Eisenstein series   We prove that if $k$ and $\ell$ are sufficiently large, then all the zeros of
the weight $k+\ell$ cusp form $E_k(z) E_{\ell}(z) - E_{k+\ell}(z)$ in the
standard fundamental domain lie on the boundary. We moreover find formulas for
the number of zeros on the bottom arc with $|z|=1$, and those on the sides with
$x = \pm 1/2$. One important ingredient of the proof is an approximation of the
Eisenstein series in terms of the Jacobi theta function.

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The categories of this paper are: hep-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: adap-org
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The categories of this paper are: nucl-th
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The categories of this paper are: hep-th
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The categories of this paper are: ao-sci
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The categories of this paper are: hep-ex
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The categories of this paper are: stat
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The categories of this paper are: acc-phys
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The categories of this paper are: comp-gas
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The categories of this paper are: bayes-an
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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: patt-sol
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The categories of this paper are: math-ph
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The categories of this paper are: alg-geom