An optimal choice of Dirichlet polynomials for the Nyman-Beurling criterion

We give a conditional result on the constant in the B\'aez-Duarte reformulation of the Nyman-Beurling criterion for the Riemann Hypothesis. We show that assuming the Riemann hypothesis and that \(\sum_{\rho}\frac{1}{|\zeta'(\rho)|^2}\ll T^{3/2-\delta}\), for some \(\delta>0\), the value of this constant coincides with the lower bound given by Burnol.