| In this talk, we discuss an intersection formula between two natural families of arithmetic cycles in the Hilbert modular surfaces over integers ---the Arithmetic Hirzebruch-Zagier cycles (dim 2) indexed by positive integers and the arithmetic CM cycles associated to quartic CM number fields. We use it to obtain a generalization of the well-known Chowla-Selberg formula to the simplest non-abelian CM number fields (non-biquadratic quartic CM number fields). |