Montgomery–Vaughan conjecture on large values of quadratic Dirichlet L-functions

Let $d$ range over fundamental discriminants with $|d|\leq X$. Write $\log_2 x=\log\log x$ and $\log_3 x=\log\log\log x$, and let $\theta$ and $\Theta$ be constants satisfying $0<\theta<\Theta<1$. Montgomery–Vaughan's conjecture. The number of such discriminants satisfying

$$L(1,\chi_d)\geq e^{\gamma}\left(\log_2|d|+\log_3|d|\right)$$

is greater than $X^{\theta}$ and less than $X^{\Theta}$. This concerns the frequency of exceptionally large values of quadratic Dirichlet $L$-functions near the conjectured extreme-value scale. The supplied source does not establish whether the conjecture has been resolved.