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EnglishLet E/Q be an elliptic curve of conductor Np with p a prime number which does not divide N, and let f be its associated newform of weight 2. Denote by f_\infty the p-adic Hida family passing though f, and by F_\infty its \Lambda-adic Saito–Kurokawa lift. The p-adic family F_\infty 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 T of size 2×2. We relate explicitly certain global points on E (coming from the theory of Darmon points) with the values of these Fourier coefficients and of their p-adic derivatives, evaluated at weight k=2.
| Titolo: | The Saito–Kurokawa lifting and Darmon points |
| Autori: | |
| Data di pubblicazione: | 2013 |
| Rivista: | |
| Abstract: | Let E/Q be an elliptic curve of conductor Np with p a prime number which does not divide N, and let f be its associated newform of weight 2. Denote by f_\infty the p-adic Hida family passing though f, and by F_\infty its \Lambda-adic Saito–Kurokawa lift. The p-adic family F_\infty 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 T of size 2×2. We relate explicitly certain global points on E (coming from the theory of Darmon points) with the values of these Fourier coefficients and of their p-adic derivatives, evaluated at weight k=2. |
| Handle: | http://hdl.handle.net/11577/2528838 |
| Appare nelle tipologie: | 01.01 - Articolo in rivista |
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