Twisted Gross-Zagier theorems

Details Twisted Gross-Zagier theorems Twisted Gross-Zagier theorems

2012-02-28

arxiv.org/abs/1202.6369v1

Canad. J. Math. 61, No. 4 (2009), 828-887

Mathematics

Number Theory

Scientific paper

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."

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