Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Non-vanishing and sign changes of Hecke eigenvalues for half-integral
  weight cusp forms   In this paper, we consider three problems about signs of the Fourier
coefficients of a cusp form $\mathfrak{f}$ with half-integral
weight:\begin{itemize}\item[--]The first negative coefficient of the sequence
$\{\mathfrak{a}\_{\mathfrak{f}}(tn^2)\}\_{n\in \N}$,\item[--]The number of
coefficients $\mathfrak{a}\_{\mathfrak{f}}(tn^2)$ of same
signs,\item[--]Non-vanishing of coefficients
$\mathfrak{a}\_{\mathfrak{f}}(tn^2)$ in short intervals and in arithmetic
progressions,\end{itemize}where $\mathfrak{a}\_{\mathfrak{f}}(n)$ is the $n$-th
Fourier coefficient of $\mathfrak{f}$ and $t$ is a square-free integersuch that
$\mathfrak{a}\_{\mathfrak{f}}(t)\not=0$.

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The categories of this paper are: atom-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-th
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The categories of this paper are: cs
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-ex
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The categories of this paper are: adap-org
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The categories of this paper are: nlin
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The categories of this paper are: q-bio
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The categories of this paper are: q-alg
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The categories of this paper are: mtrl-th
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The categories of this paper are: alg-geom
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The categories of this paper are: physics
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The categories of this paper are: chem-ph
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The categories of this paper are: funct-an