Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: When Kloosterman sums meet Hecke eigenvalues   By elaborating a two-dimensional Selberg sieve with asymptotics and
equidistributions of Kloosterman sums from $\ell$-adic cohomology, as well as a
Bombieri--Vinogradov type mean value theorem for Kloosterman sums in arithmetic
progressions, it is proved that for any given primitive Hecke--Maass cusp form
of trivial nebentypus, the eigenvalue of the $n$-th Hecke operator does not
coincide with the Kloosterman sum $\mathrm{Kl}(1,n)$ for infinitely many
squarefree $n$ with at most $100$ prime factors. This provides a partial
negative answer to a problem of Katz on modular structures of Kloosterman sums.

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The categories of this paper are: funct-an
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The categories of this paper are: q-fin
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The categories of this paper are: hep-ph
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The categories of this paper are: econ
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The categories of this paper are: cmp-lg
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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: acc-phys
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The categories of this paper are: astro-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: stat
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The categories of this paper are: q-alg
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The categories of this paper are: adap-org
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The categories of this paper are: comp-gas
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The categories of this paper are: mtrl-th
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The categories of this paper are: hep-lat