Families of Selberg zeta functions indexed by the Teichmueller space

To every compact hyperbolic surface endowed with a fixed spin structure, one can associate an entire function defined as an infinite product over the lengths of closed geodesics. The divisor of this Selberg zeta function is, essentially, the spectrum of the Dirac operator. The zeta function is thus a map from the Teichmueller space into the space of entire functions. We aim to prove that this map extends smoothly at certain points on the boundary of the Teichmueller space corresponding to complete hyperbolic surfaces with cusps.