  After Voronin proved the universality theorem of the Riemann zeta function in
the 1970s, universality theorems have been proposed for various zeta and
L-functions. Drungilas-Garunkstis-Kacenas' work at 2013 on the universality
theorem of the Selberg zeta function for the modular group is one of them and
is probably the first universality theorem of the zeta function of order
greater than one. Recently, Mishou (2021) extended it by proving the joint
universality theorem for the principal congruence subgroups. In the present
paper, we further extend these works by proving the (joint) universality
theorem for subgroups of the modular group and co-compact arithmetic groups
derived from indefinite quaternion algebras, which is available in the region
wider than the regions in the previous two works.
