Numerical computations concerning Landau-Siegel zeros

Rick F. Lu, Asif Zaman, Haonan Zhao

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