Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The distribution of the logarithm in an orthogonal and a symplectic
  family of $L$-functions   We consider the logarithm of the central value $\log L(1/2)$ in the
orthogonal family ${L(s,f)}_{f \in H_k}$ where $H_k$ is the set of weight $k$
Hecke-eigen cusp form for $SL_2(\mathbb{Z})$, and in the symplectic family
${L(s,\chi_{8d})}_{d \asymp D}$ where $\chi_{8d}$ is the real character
associated to fundamental discriminant $8d$. Unconditionally, we prove that the
two distributions are asymptotically bounded above by Gaussian distributions,
in the first case of mean $-\frac{1}{2} \log \log k$ and variance $\log \log
k$, and in the second case of mean $\frac{1}{2}\log \log D$ and variance $\log
\log D$. Assuming both the Riemann and Zero Density Hypotheses in these
families we obtain the full normal law in both families, confirming a
conjecture of Keating and Snaith.

32
The categories of this paper are: atom-ph
31
The categories of this paper are: ao-sci
13
The categories of this paper are: quant-ph
36
The categories of this paper are: cmp-lg
8
The categories of this paper are: hep-ex
35
The categories of this paper are: mtrl-th
27
The categories of this paper are: comp-gas
17
The categories of this paper are: q-fin
0
The categories of this paper are: hep-ph
5
The categories of this paper are: gr-qc
33
The categories of this paper are: plasm-ph
21
The categories of this paper are: adap-org
9
The categories of this paper are: nlin
20
The categories of this paper are: acc-phys
16
The categories of this paper are: stat
11
The categories of this paper are: hep-lat