The theorems of Gross–Zagier and Zhang relate the Neron–Tate heights of complex mul-tiplication points on the modular curve X_0 (N) (and on Shimura curve analogues) with the centralderivatives of automorphic L-function. We extend these results to include certain CM points on mod-ular curves of the form X(F_0 (M) nF_1(S))(and on Shimura curve analogues). These results are mo-tivated by applications to Hida theory that can be found in the companion article "Central derivativesof L-functions in Hida families", Math. Ann. 399(2007), 803-818.
展开▼
