A mollification problem

Baez-Duarte [ arXiv:math.NT/0202141] has recently proven that the Riemann Hypothesis is equivalent to the assertion that

\begin{displaymath}\inf_{A_N(s)}\int_{-\infty}^\infty \vert 1-A_N(1/2+it)\zeta(1/2+it\vert^2)~\frac {dt}{\frac 14 +t^2}\end{displaymath}

tends to 0 as $N\to \infty$ where $A_N(s)$ can be any Dirichlet polynomial of length $N$:

\begin{displaymath}A_N(s)=\sum_{n=1}^N \frac {a_n}{n^s}.\end{displaymath}

Previously, Baez-Duarte, Balazard, Landreaux, and Saias had noted that as a consequence of the Nyman-Beurling criterion, the above assertion implies RH.

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