Twisted Gross–Zagier Theorems

Howard, Benjamin

Canadian journal of mathematics, Tome 61 (2009) no. 4, pp. 828-887

Résumé

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.

Détail

DOI : 10.4153/CJM-2009-044-1

Mots-clés : 11G18, 14G35

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