Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Extreme values of the argument of the Riemann zeta function   Let $S(t) =
\frac{1}{\pi}\operatorname{Im}\log\zeta\left(\frac{1}{2}+it\right)$. Using
Soundararajan's resonance method we prove an unconditional lower bound on the
size of the tails of the distribution of $S(t)$. In particular we reproduce the
best unconditional $\Omega$ result for $S(t)$ which is due to Tsang, \[ S(t) =
\Omega_\pm\left(\left(\frac{\log t}{\log \log t}\right)^{1/3}\right), \] and
get a bound on how often large values of $S(t)$ occur. We also give a
probabilistic argument for why this $\Omega$ result may be the best possible
given our current knowledge of the zeros of the zeta function.

18
The categories of this paper are: econ
9
The categories of this paper are: nlin
22
The categories of this paper are: chao-dyn
12
The categories of this paper are: nucl-th
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The categories of this paper are: dg-ga
30
The categories of this paper are: q-alg
27
The categories of this paper are: comp-gas
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The categories of this paper are: stat
17
The categories of this paper are: q-fin
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The categories of this paper are: alg-geom
0
The categories of this paper are: hep-ph
8
The categories of this paper are: hep-ex
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The categories of this paper are: acc-phys
35
The categories of this paper are: mtrl-th
5
The categories of this paper are: gr-qc
31
The categories of this paper are: ao-sci