James Parks: A transition in the Ratios Conjecture

In this talk we discuss the 1-level density of low-lying zeros of
quadratic Dirichlet L-function. Under the assumption of the L-functions Ratios
Conjecture we observe a transition in the main term as was predicted by the
Katz-Sarnak heuristic as well as in the lower order terms when the support of
the Fourier transform of the corresponding even test function $\phi$ reaches
the point 1. This transition is also observed under GRH  when $\widehat \phi$
reaches 1. (Joint work with D. Fiorilli and A. Södergren)