Large values of quadratic Dirichlet $L$-functions near the central point

Abstract

In this paper, we investigate the conditional large values of the quadratic Dirichlet $L$-functions near the central point $s=1/2$. When $\sigma$ closes to $1/2$ within a suitable range, we show that $L(\sigma ,{\chi }_d)$ have the conditional large values of the similar order of magnitude as $L(1/2,{\chi }_d)$.