An explicit upper bound for Siegel zeros of imaginary quadratic fields

Abstract

For any integer $d\geq 3$ 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]. $