a la me moire de gian-carlo rota Let \(t) denote the fractional part of t, H the Hilbert space L 2 (0, + ), B the subspace of H of functions f (t)= n k=1 c k \(% k Ât), where n # N, c k # C, and 0<% k 1 for 1 k n, / the characteristic function of ]0, 1] and D(*) the distance in H between / and B * , the subspace of B of functions f such that all % k *. A well-known result of B. Nyman and A. Beurling implies that the Riemann hypothesis is equivalent to the statement lim * Ä 0 D(*)=0. We prove here that inf 0<*<1 D(*) -log(2Â*)>0, and we conjecture that lim * Ä 0 D(*) -log(1Â*)=
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