Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Signs of Fourier Coefficients of Hecke-Maass Cusp Forms on
  $\mathrm{GL}_3$   We consider sign changes of Fourier coefficients of Hecke-Maass cusp forms
for the group $\mathrm{SL}_3(\mathbb Z)$. When the underlying form is
self-dual, we show that there are $\gg_\varepsilon X^{5/6-\varepsilon}$ sign
changes among the coefficients $\{A(m,1)\}_{m\leq X}$ and that there is a
positive proportion of sign changes for many self-dual forms. Similar result
concerning the positive proportion of sign changes also hold for the
real-valued coefficients $A(m,m)$ for generic $\mathrm{GL}_3$ cusp forms, a
result which is based on a new effective Sato-Tate type theorem for a family of
$\mathrm{GL}_3$ cusp forms we establish. In addition, non-vanishing of the
Fourier coefficients is studied under the Ramanujan-Petersson conjecture.

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The categories of this paper are: funct-an
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The categories of this paper are: chao-dyn
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The categories of this paper are: stat
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The categories of this paper are: econ
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The categories of this paper are: cs
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The categories of this paper are: eess
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The categories of this paper are: gr-qc
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The categories of this paper are: bayes-an
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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: dg-ga
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The categories of this paper are: astro-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: hep-th
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The categories of this paper are: acc-phys
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The categories of this paper are: nucl-th