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

tends to 0 as where can be any Dirichlet polynomial of length :

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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