Numerical Computations Concerning Landau-Siegel Zeros

Rick F. Lu, Asif Zaman, Haonan Zhao

We computationally verify that if $L(s,\ddot{I}‡)$ is a quadratic Dirichlet $L$-function modulo $q\le 10^{10}$ then $L(\ddot{I}ƒ,\ddot{I}‡)\ne 0$ for real $\ddot{I}ƒ\ge 1-1/(5\log q)$. The number of verif…