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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'szeta function for the modular groups in the critical strip. The present paperstudies the growth of its square integral for the modular group, co-compactarithmetic groups derived from indefinite quaternion algebras and theirsubgroups.

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