  For any congruence subgroup of the modular group, we extend the region of
convergence of the Euler products of the Selberg zeta functions beyond the
boundary Re s = 1, if they are attached with a nontrivial irreducible unitary
representation. The region is determined by the size of the lowest eigenvalue
of the Laplacian, and it extends to Re s $\geqslant$ 3/4 under Selberg's
eigenvalue conjecture. More generally, for any unitary representation we
establish the relation between the behavior of partial Euler products in the
critical strip and the estimate of the error term in the prime geodesic
theorem. For the trivial representation, the proof essentially exploits the
idea of the celebrated work of Ramanujan.
