  The goal of this paper is to prove a formula expressing the modular height of
a quaternionic Shimura curve over a totally real number field in terms of the
logarithmic derivative of the Dedekind zeta function of the totally real number
field. Our proof is based on the work of Yuan-Zhang-Zhang on the Gross-Zagier
formula and the work of Yuan-Zhang on the averaged Colmez conjecture. All these
works are in turn inspired by the Pioneering work of Gross-Zagier and some
philosophies of Kudla's program.
