Landau-Siegel zeros over a base field and effective Brauer-Siegel

William D. Banks

Let $k$ be a number field. We prove that for every quadratic extension $F/k$, every real zero $\beta \in (0,1)$ of $L(s,{\chi }_{F/k})$ satisfies $(1-\beta )\log d_F\ge c(k)$ with an effective cons…