Low-lying zeros of L-functions and random matrix theory

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Linear statistics of low-lying zeros of L-functions (2002, background): “For example, in the case of quadratic L–functions mock-Gaussian behaviour can be deduced from the work of Rubinstein [17].”
Sato–Tate theorem for families and low-lying zeros of automorphic $$L$$L-functions (2012, background): “In a large number of cases, and with high accuracy, the distribution of non-trivial zeros of automorphic L-functions coincide with the distribution of eigenvalues of random matrices (see [38, 84] for numerical investigations and conjectures and see [41, 49, 50, 53, 68, 81, 83] and the references her”
Low-lying zeros of families of elliptic curves (2004, methodology): “In general we can handle the first sum as long as all of the irreducible factors of R(r) are of degree 3 or less. Proof. Suppose R (d) is as above.”
How to generate random matrices from the classical compact groups (2006, background): “ting matrices in the COE and CSE, but are also important ensembles in their own right. Indeed, the work of Montgomery [11], Odlyzko [12], Katz and Sarnak [6], Keating and Snaith [7, 8] and Rubinstein [13] has shown beyond doubt that the local statistical properties of the Howtogeneraterandomunitarym”
n -level density of the low-lying zeros of quadratic Dirichlet L -functions. (2008, methodology): “This is exactly what was carried out in Rubinstein’s work [21].”