Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Dirichlet-Bohr radius   Denote by $\Omega(n)$ the number of prime divisors of $n \in \mathbb{N}$
(counted with multiplicities). For $x\in \mathbb{N}$ define the Dirichlet-Bohr
radius $L(x)$ to be the best $r>0$ such that for every finite Dirichlet
polynomial $\sum_{n \leq x} a_n n^{-s}$ we have $$ \sum_{n \leq x} |a_n|
r^{\Omega(n)} \leq \sup_{t\in \mathbb{R}} \big|\sum_{n \leq x} a_n
n^{-it}\big|\,. $$ We prove that the asymptotically correct order of $L(x)$ is
$ (\log x)^{1/4}x^{-1/8} $. Following Bohr's vision our proof links the
estimation of $L(x)$ with classical Bohr radii for holomorphic functions in
several variables. Moreover, we suggest a general setting which allows to
translate various results on Bohr radii in a systematic way into results on
Dirichlet-Bohr radii, and vice versa.

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The categories of this paper are: physics
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The categories of this paper are: econ
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The categories of this paper are: hep-lat
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The categories of this paper are: funct-an
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The categories of this paper are: q-alg
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The categories of this paper are: bayes-an
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The categories of this paper are: alg-geom
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The categories of this paper are: nucl-ex
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The categories of this paper are: nucl-th
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The categories of this paper are: solv-int
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The categories of this paper are: mtrl-th
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The categories of this paper are: eess
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The categories of this paper are: chao-dyn
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The categories of this paper are: plasm-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: stat