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Twisted Gross–Zagier Theorems

Published online by Cambridge University Press:  20 November 2018

Benjamin Howard
Benjamin Howard*
Affiliation:
Department of Mathematics, Boston College, Chestnut Hill, MA 02467, USA, e-mail: [email protected]
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Abstract

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The theorems of Gross–Zagier and Zhang relate the Néron–Tate heights of complex multiplication points on the modular curve ${{X}_{0}}\,(N)$ (and on Shimura curve analogues) with the central derivatives of automorphic $L$-function. We extend these results to include certain CM points on modular curves of the form $X({{\Gamma }_{0}}(M)\bigcap {{\Gamma }_{1}}(S))$ (and on Shimura curve analogues). These results are motivated by applications to Hida theory that can be found in the companion article “Central derivatives of $L$ -functions in Hida families”, Math. Ann. 399(2007), 803–818.

Keywords

11G1814G35
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 61 , Issue 4 , 01 August 2009 , pp. 828 - 887
Copyright
Copyright © Canadian Mathematical Society 2012

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