An explicit upper bound for Siegel zeros of imaginary quadratic fields

Abstract

For any integer $d\ge 3$ such that $-d$ is a fundamental discriminant, we show that the Dirichlet $L$-function associated with the real primitive character $\chi (\cdot )=(\frac{-d}{\cdot })$ does not vanish on the positive part of the interval $[1-6.5/\sqrt{d},1].$

18 pages, 2 figures