One-level density estimates for Dirichlet L-functions with extended support

We estimate the 1-level density of low-lying zeros of L(s, chi) with chi ranging over primitive Dirichlet characters of conductor in [1/2 Q, Q] and for test functions whose Fourier transform is supported in (-2 -50/1093, 2 + 50/1093). Previously, any extension of the support past the range (-2, 2) was only known conditionally on deep conjectures about the distribution of primes in arithmetic progressions, beyond the reach of the generalized Riemann hypothesis (e.g., Montgomery's conjecture). Our work provides the first example of a family of L-functions in which the support is unconditionally extended past the "diagonal range" that follows from a straightforward application of the underlying trace formula (in this case orthogonality of characters). We also highlight consequences for nonvanishing of L(s, chi).