{"paper":{"title":"The Saito-Kurokawa lifting and Darmon points","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Marc-Hubert Nicole, Matteo Longo","submitted_at":"2012-01-17T14:06:40Z","abstract_excerpt":"Let $E_{/_\\Q}$ be an elliptic curve of conductor $Np$ with $p\\nmid N$ 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 $\\{\\widetilde A_T(k)\\}_T$ indexed by positive definite symmetric half-integral matrices $T$ of size $2\\times 2$. We relate explicitly certain global points on $E$ (coming from the theory of Stark-"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.3515","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}