<italic>n</italic>-level density of the low-lying zeros of quadratic Dirichlet <italic>L</italic>-functions.

Abstract

The GUE Conjecture of Montgomery provides the first evidence in favor of the spectral interpretation of the non-trivial zeros of the Riemann zeta-function. Rather than being universally GUE, the Density Conjecture of Katz and Sarnak further associates a classical compact group to each reasonable family of <italic>L</italic>-function. In this thesis, we study the <italic> n</italic>-level density of the low-lying zeros of quadratic Dirichlet <italic> L</italic>-functions. Our results provide further support to the Density Conjecture.