Low-lying zeros of quadratic Dirichlet L-functions, hyper-elliptic curves and Random Matrix Theory

Alexei Entin, Edva Roditty-Gershon, Zeev Rudnick

The statistics of low-lying zeros of quadratic Dirichlet L-functions were conjectured by Katz and Sarnak to be given by the scaling limit of eigenvalues from the unitary symplectic…