Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Moments of polynomials with random multiplicative coefficients   For $X(n)$ a Rademacher or Steinhaus random multiplicative function, we
consider the random polynomials $$ P_N(\theta) = \frac1{\sqrt{N}} \sum_{n\leq
N} X(n) e(n\theta), $$ and show that the $2k$-th moments on the unit circle $$
\int_0^1 \big| P_N(\theta) \big|^{2k}\, d\theta $$ tend to Gaussian moments in
the sense of mean-square convergence, uniformly for $k \ll (\log N / \log \log
N)^{1/3}$, but that in contrast to the case of i.i.d. coefficients, this
behavior does not persist for $k$ much larger. We use these estimates to (i)
give a proof of an almost sure Salem-Zygmund type central limit theorem for
$P_N(\theta)$, previously obtained in unpublished work of Harper by different
methods, and (ii) show that asymptotically almost surely $$ (\log N)^{1/6 -
\varepsilon} \ll \max_\theta |P_N(\theta)| \ll \exp((\log
N)^{1/2+\varepsilon}), $$ for all $\varepsilon > 0$.

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The categories of this paper are: funct-an
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The categories of this paper are: alg-geom
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The categories of this paper are: cond-mat
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The categories of this paper are: adap-org
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The categories of this paper are: nucl-ex
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The categories of this paper are: patt-sol
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The categories of this paper are: physics
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The categories of this paper are: hep-ex
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The categories of this paper are: ao-sci
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The categories of this paper are: dg-ga
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The categories of this paper are: chem-ph
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The categories of this paper are: econ
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The categories of this paper are: astro-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: q-fin
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The categories of this paper are: gr-qc