  In this note we study the thermodynamic formalism for the positive geodesic
flow on the modular surface. We define the pressure and prove the variational
principle. We also establish conditions for the the pressure to be real
analytic and for the potentials to have unique equilibrium states. The results
in this paper were largely superceded by "Phase transitions for suspension
flows" by Iommi and Jordan arXiv:1202.0849
