  The partition function of a bosonic Riemann gas is given by the Riemann zeta
function. We assume that the hamiltonian of this gas at a given temperature
$\beta^{-1}$ has a random variable $\omega$ with a given probability
distribution over an ensemble of hamiltonians. We study the average free energy
density and average mean energy density of this arithmetic gas in the complex
$\beta$-plane. Assuming that the ensemble is made by an enumerable infinite set
of copies, there is a critical temperature where the average free energy
density diverges due to the pole of the Riemann zeta function. Considering an
ensemble of non-enumerable set of copies, the average free energy density is
non-singular for all temperatures, but acquires complex values in the critical
region. Next, we study the mean energy density of the system which depends
strongly on the distribution of the non-trivial zeros of the Riemann zeta
function. Using a regularization procedure we prove that the this quantity is
continuous and bounded for finite temperatures.
