Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Extremal bounds for Dirichlet polynomials with random multiplicative
  coefficients   For $X(n)$ a Steinhaus random multiplicative function, we study the maximal
size of the random Dirichlet polynomial $$ D_N(t) = \frac1{\sqrt{N}} \sum_{n
\leq N} X(n) n^{it}, $$ with $t$ in various ranges. In particular, for fixed
$C>0$ and any small $\varepsilon>0$ we show that, with high probability, $$
  \exp( (\log N)^{1/2-\varepsilon} ) \ll \sup_{|t| \leq N^C} |D_N(t)| \ll \exp(
(\log N)^{1/2+\varepsilon}). $$

10
The categories of this paper are: q-bio
35
The categories of this paper are: mtrl-th
34
The categories of this paper are: chem-ph
13
The categories of this paper are: quant-ph
9
The categories of this paper are: nlin
31
The categories of this paper are: ao-sci
28
The categories of this paper are: alg-geom
33
The categories of this paper are: plasm-ph
7
The categories of this paper are: hep-th
3
The categories of this paper are: physics
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The categories of this paper are: acc-phys
18
The categories of this paper are: econ
8
The categories of this paper are: hep-ex
37
The categories of this paper are: supr-con
30
The categories of this paper are: q-alg
22
The categories of this paper are: chao-dyn