Square integrals of the logarithmic derivatives of Selberg's zeta functions in the critical strip

Abstract

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.