  I show how Bose-Einstein condensation (BEC) in a non interacting bosonic
system with exponential density of states function yields to a new class of
Lerch zeta functions. By looking on the critical temperature, I suggest that a
possible strategy to prove the "Riemann hypothesis" problem. In a theorem and a
lemma I suggested that the classical limit $\hbar\to 0$ of BEC can be used as a
tool to find zeros of real part of the Riemann zeta function with complex
argument. It reduces the Riemann hypothesis to a softer form. Furthermore I
propose a pair of creation-annihilation operators for BEC phenomena. This set
of creation-annihilation operators is defined on a complex Hilbert space. They
build a set up to interpret this type of BEC as a creation-annihilation
phenomenon for a virtual hypothetical particle.
