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

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