Surpassing the ratios conjecture in the 1-level density of Dirichlet<i>L</i>-functions
Surpassing the ratios conjecture in the 1-level density of Dirichlet<i>L</i>-functions
We study the $1$-level density of low-lying zeros of Dirichlet $L$-functions in the family of all characters modulo $q$, with $Q/2 < q\leq Q$. For test functions whose Fourier transform is supported in $(-3/2, 3/2)$, we calculate this quantity beyond the square-root cancellation expansion arising from the $L$-function Ratios Conjecture …