Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The distribution of the $L_4$ norm of Littlewood polynomials   Classical conjectures due to Littlewood, Erd\H{o}s and Golay concern the
asymptotic growth of the $L_p$ norm of a Littlewood polynomial (having all
coefficients in $\{1, -1\}$) as its degree increases, for various values of
$p$. Attempts over more than fifty years to settle these conjectures have
identified certain classes of the Littlewood polynomials as particularly
important: skew-symmetric polynomials, reciprocal polynomials, and negative
reciprocal polynomials. Using only elementary methods, we find an exact formula
for the mean and variance of the $L_4$ norm of polynomials in each of these
classes, and in the class of all Littlewood polynomials. A consequence is that,
for each of the four classes, the normalized $L_4$ norm of a polynomial drawn
uniformly at random from the class converges in probability to a constant as
the degree increases.

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The categories of this paper are: comp-gas
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The categories of this paper are: acc-phys
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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: supr-con
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The categories of this paper are: hep-ph
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The categories of this paper are: stat
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The categories of this paper are: math-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: chao-dyn
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The categories of this paper are: solv-int
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The categories of this paper are: econ
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The categories of this paper are: adap-org
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The categories of this paper are: q-bio
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The categories of this paper are: hep-lat
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The categories of this paper are: astro-ph