  In our previous work (https://doi.org/10.1002/mana.202000268, Math. Nachr.,
2021), we proposed an upper bound of the logarithmic derivative of Selberg's
zeta function for the modular groups in the critical strip. The present paper
studies the growth of its square integral for the modular group, co-compact
arithmetic groups derived from indefinite quaternion algebras and their
subgroups.
