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

Abstract

We give a conditional result on the constant in the Báez-Duarte reformulation of the Nyman-Beurling criterion for the Riemann Hypothesis. We show that assuming the Riemann hypothesis and that ${\sum }_{\rho }\frac{1}{|{\zeta }^{\prime }(\rho ){|}^2}\ll T^{3/2-\delta }$, for some $\delta >0$, the value of this constant coincides with the lower bound given by Burnol.

arXiv comment9 pages

References in corpus (1)

• A lower bound in an approximation problem involving the zeros of the Riemann zeta function