Lower order terms in the 1-level density for families of holomorphic cuspidal newforms

The Katz-Sarnak density conjecture states that, in the limit as the nconductors tend to infinity, the behavior of normalized zeros near the central npoint of families of L-functions agree with the N -> oo scaling limits of neigenvalues near 1 of subgroups of U(N). Evidence for this has been found for nmany families by studying the n-level densities; for..