201211.5191v1 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 ∑ρ1|ζ′(ρ)|2≪T3/2−δ, for some δ>0, the value of this constant coincides with the lower bound given by Burnol.