The Saito–Kurokawa lifting and Darmon points

Let be an elliptic curve of conductor with and let be its associated newform of weight . Denote by the -adic Hida family passing though , and by its -adic Saito–Kurokawa lift. The -adic family of Siegel modular forms admits a formal Fourier expansion, from which we can define a family of normalized...

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Bibliographic Details
Published in:Mathematische annalen 2013-06, Vol.356 (2), p.469-486
Main Authors: Longo, Matteo, Nicole, Marc-Hubert
Format: Article
Language:English
Subjects:
Mathematics
Mathematics and Statistics
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Summary:Let be an elliptic curve of conductor with and let be its associated newform of weight . Denote by the -adic Hida family passing though , and by its -adic Saito–Kurokawa lift. The -adic family of Siegel modular forms admits a formal Fourier expansion, from which we can define a family of normalized Fourier coefficients indexed by positive definite symmetric half-integral matrices of size . We relate explicitly certain global points on (coming from the theory of Darmon points) with the values of these Fourier coefficients and of their -adic derivatives, evaluated at weight .
ISSN:0025-5831
1432-1807
DOI:10.1007/s00208-012-0846-5