Bose-Einstein Condensation for an Exponential Density of States Function and Lerch Zeta Function

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.