  We propose a consistent quantization of the Berry-Keating Hamiltonian x p,
which is currently discussed in connection with the non trivial zeros of the
Riemann zeta function. The smooth part of the Riemann counting formula of the
zeros is reproduced exactly. The zeros appear, not as eigenstates, but as
missing states in the spectrum, in agreement with Connes adelic approach to the
Riemann hypothesis. The model is exactly solvable and renormalizable, with a
cyclic Renormalization Group. These results are obtained by mapping the
Berry-Keating model into the Russian doll model of superconductivity. Finally,
we propose a generalization of these models in an attempt to explain the
oscillatory part of the Riemann's formula.
