Sur la nature non-cyclotomique des points d'ordre fini des courbes elliptiques. (On the noncyclotomic nature of finite-order points of elliptic curves). With an appendix by E. Kowalski and P. Michel

DOI10.1215/S0012-7094-01-11013-2zbMath1020.11041MaRDI QIDQ1847870

Loic Merel

Publication date: 27 October 2002

Published in: Duke Mathematical Journal (Search for Journal in Brave)

zbMATH Keywords

elliptic curvesmodular curvesNéron modelHecke algebraEisenstein ideal

Mathematics Subject Classification ID

Rational points (14G05) Elliptic curves over global fields (11G05) (L)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture (11G40) Estimates on character sums (11L40)

Related Items (8)

Elliptic curves with abelian division fields ⋮ Rational points on \(X_0^+(p^r)\) ⋮ Elliptic curves with \(\mathbb Q({\mathcal E}[3)=\mathbb Q(\zeta_3)\) and counterexamples to local-global divisibility by 9] ⋮ On the minimal set for counterexamples to the local-global principle ⋮ Petersson products of modular forms associated with the values of \(L\)-functions ⋮ Triviality of \(X_{\text{split}}(N)(\mathbb Q)\) for certain congruence classes of \(N\) ⋮ Families of \(L\)-functions of automorphic forms and applications ⋮ On the torsion of Drinfeld modules of rank two

Cites Work

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• L'accouplement de Weil entre le sous-groupe de Shimura et le sous-groupe cuspidal de J0(p).
• On Character Sums and L -Series. II
• Two non-vanishing theorems of special values of \(L\)-functions

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