Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Exponential sums of the M\"{o}bius function and flat polynomials   We present an elementary problem on analytic polynomials with coefficients
$\pm 1$ or in $\{0,\pm 1 \}$ which implies Riemann hypothesis. It is turns out
that this problem is a particular case of the weak form of a flat polynomials
problem asked by Erd\"os in his 1957's paper. We provide also under an
extra-condition the converse.

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The categories of this paper are: nlin
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The categories of this paper are: plasm-ph
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The categories of this paper are: hep-th
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The categories of this paper are: physics
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The categories of this paper are: supr-con
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The categories of this paper are: alg-geom
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The categories of this paper are: econ
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The categories of this paper are: bayes-an
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The categories of this paper are: patt-sol
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The categories of this paper are: q-fin
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-lat
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The categories of this paper are: atom-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: chao-dyn
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The categories of this paper are: nucl-ex