Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Strong Szego asymptotics and zeros of the zeta function   Assuming the Riemann hypothesis, we prove the weak convergence of linear
statistics of the zeros of L-functions towards a Gaussian field, with
covariance structure corresponding to the $\HH^{1/2}$-norm of the test
functions. For this purpose, we obtain an approximate form of the explicit
formula, relying on Selberg's smoothed expression for $\zeta'/\zeta$ and the
Helffer-Sj\"ostrand functional calculus. Our main result is an analogue of the
strong Szeg{\H o} theorem, known for Toeplitz operators and random matrix
theory.

18
The categories of this paper are: econ
36
The categories of this paper are: cmp-lg
20
The categories of this paper are: acc-phys
4
The categories of this paper are: cond-mat
21
The categories of this paper are: adap-org
17
The categories of this paper are: q-fin
8
The categories of this paper are: hep-ex
37
The categories of this paper are: supr-con
1
The categories of this paper are: cs
30
The categories of this paper are: q-alg
24
The categories of this paper are: dg-ga
3
The categories of this paper are: physics
25
The categories of this paper are: patt-sol
23
The categories of this paper are: solv-int
29
The categories of this paper are: funct-an
16
The categories of this paper are: stat