  In this note concerning integrals involving the logarithm of the Riemann Zeta
function, we extend some treatments given in previous pioneering works on the
subject and introduce a more general set of Lorentz measures. We first obtain
two new equivalent formulations of the Riemann Hypothesis (RH). Then with a
special choice of the measure we formulate the RH as a ``hidden symmetry'', a
global symmetry which connects the region outside the critical strip with that
inside the critical strip. The Zeta function with all the primes appears as
argument of the Zeta function in the critical strip. We then illustrate the
treatment by a simple numerical experiment. The representation we obtain go a
little more in the direction to believe that RH may eventually be true.
