The n-level densities of low-lying zeros of quadratic Dirichlet L-functions
Previous work by Rubinstein and Gao computed the n-level densities for families of quadratic Dirichlet L-functions for test functions f̂₁, ..., f̂ₙ supported in , and showed agreement with random matrix theory predictions in this range for n ≤ 3 but only in a restricted range for larger n. We extend these results and show agreement for n ≤ 7, and reduce higher n to a Fourier transform identity. The proof involves adopting a new combinatorial perspective to convert all terms to a canonical form,...