On an analytic estimate in the theory of the Riemann Zeta function and a Theorem of Baez-Duarte

We establish a uniform upper estimate for the values of zeta(s)/zeta(s+A), 0<= A, on the critical line (conditionally on the Riemann Hypothesis). We use this to give a variant, purely complex analytic, to Baez-Duarte’s proof of a strengthened Nyman-Beurling criterion for the validity of the Riemann Hypothesis.