  The theorems of Gross-Zagier and Zhang relate the N\'eron-Tate heights of
complex multiplication points on the modular curve X_0(N) (and on Shimura curve
analogues) with the central derivatives of automorphic L-functions. We extend
these results to include certain CM points on Shimura curves of higher level
structure. These results are motivated by applications to Hida theory which are
described in the companion article "Central derivatives of L-functions in Hida
families."
