Montgomery's conjecture on Dirichlet polynomials

Let $N\geq 1$, $T>0$, and let $B_T$ be any ball of radius $T$. For coefficients $\{b_n\}_{n=N+1}^{2N}\subset\mathbb{C}$, write

$$\sum_{n=N+1}^{2N} b_n n^{it}$$

for the associated Dirichlet polynomial, and let $\|b_n\|_{\ell^\infty}$ denote the supremum of the coefficients. Montgomery's conjecture. For every $p\geq 2$ and every $\varepsilon>0$,

$$\left\|\sum_{n=N+1}^{2N} b_n n^{it}\right\|_{L^p(B_T)} \leq C_\varepsilon T^\varepsilon N^{1/2}\left(N^{p/2}+T\right)^{1/p}\|b_n\|_{\ell^\infty}.$$

This is the conjecture on Dirichlet-polynomial mean values that motivates the paper's decoupling approach; the supplied source does not state whether it has been resolved, so its status remains open here.