The classical Jensen’s formula is a well-known theorem of complex analysis which characterizes, for a meromorphic function f on the unit disc, the value of the integral of log|f(z)| on the unit circle in terms of the zeros and poles of f inside the unit disc. An important theorem of Rohrlich establishes a version of Jensen’s formula for modular functions f with respect to the full modular group PSL_2(Z) and expresses the integral of log|f(z)| over the corresponding modular curve in terms of special values of Dedekind’s eta function.

In this talk I will present a Jensen–Rohrlich type formula for certain family of functions defined in the hyperbolic 3-space which are automorphic for the group PSL_2(O_K) where O_K denotes the ring of integers of an imaginary quadratic field.

This is joint work with O. Imamoglu (ETH Zurich), A.-M. von Pippich (TU Darmstadt) A. Toth (Eotvos Lorand Univ.).