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

摘要

We slightly improve the lower bound of Wez-Duarte, Balazard, Landreau and Saias in the Nyman-Beurling formulation of the Riemann Hypothesis as an approximation problem. We construct Hilbert space vectors which could prove useful in the context of the so-called "Hilbert-Polya idea". (C) 2002 Elsevier Science (USA). [References: 18]