Universality theorems of Selberg zeta functions for arithmetic groups

We prove a universality theorem for the Selberg zeta function of subgroups of SL₂(Z) or co-compact arithmetic groups derived from quaternion algebras, in the strip \5/6 < Res < 1\, improving the range compared with a previous work by Drungilas–Garunkštis–Kačenas. We also obtain the same range for a joint universality theorem for congruence subgroups, which improves a result by Mishou.