Sur le rang des courbes elliptiques sur les corps de classes de Hilbert

DOI10.1112/S0010437X10005051zbMath1276.11096MaRDI QIDQ5199358

Nicolas Templier

Publication date: 16 August 2011

Published in: Compositio Mathematica (Search for Journal in Brave)

zbMATH Keywords

elliptic curves\(L\)-functionsautomorphic formsequidistributionHeegner points

Mathematics Subject Classification ID

Elliptic curves over global fields (11G05) Complex multiplication and moduli of abelian varieties (11G15) (L)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture (11G40) Arithmetic varieties and schemes; Arakelov theory; heights (14G40)

Related Items (5)

Lower bounds for ranks of elliptic curves ⋮ Non-split sums of coefficients of \(\mathrm{GL}(2)\)-automorphic forms ⋮ Wide moments of L-functions. I: Twists by class group characters of imaginary quadratic fields ⋮ Horizontal non-vanishing of Heegner points and toric periods ⋮ Intersection of class fields

Cites Work

• Unnamed Item
• Gross-Zagier formula for \(\text{GL}_ 2\).
• Asymptotic behaviour for the averaged height of Heegner points
• Independence of points on elliptic curves arising from special points on modular and Shimura curves. I: Global results
• On the L-functions of canonical Hecke characters of imaginary quadratic fields. II
• Heegner points and derivatives of \(L\)-series
• Hyperbolic distribution problems and half-integral weight Maass forms
• Equidistribution of small points on abelian varieties
• Positivity and discretion of algebraic points of curves
• The non-vanishing of certain Hecke \(L\)-functions at the center of the critical strip
• On the L-functions of canonical Hecke characters of imaginary quadratic fields
• Galois conjugacy of unramified twists of Hecke characters
• Mean values of derivatives of modular \(L\)-series
• Test vectors for linear forms
• Equidistribution of small points
• Mazur's conjecture on higher Heegner points.
• Non-triviality of Heegner points
• The subconvexity problem for Rankin-Selberg \(L\)-functions and equidistribution of Heegner points
• Arithmetic of Weil curves
• Special values of anticyclotomic \(L\)-functions.
• Modular elliptic curves and Fermat's Last Theorem
• Ring-theoretic properties of certain Hecke algebras
• Class group \(L\)-functions
• Relating invariant linear form and local epsilon factors via global methods. (With an appendix by Hiroshi Saito)
• Lower bounds for ranks of elliptic curves
• On the independence of Heegner points associated to distinct quadratic imaginary fields
• Nonvanishing theorems for L-functions of modular forms and their derivatives
• On the modularity of elliptic curves over 𝐐: Wild 3-adic exercises
• Local ε-Factors and Characters of GL(2)
• Hauteur asymptotique des points de Heegner
• The Arithmetic of Elliptic Curves
• Local Orders, Root Numbers, and Modular Curves
• On the order of vanishing of modular $L$-functions at the critical point
• Heights of Heegner points on Shimura curves.
• Integration on \({\mathcal H_p}\times\mathcal H\) and arithmetic applications.
• Non-triviality of CM points in ring class field towers. With an appendix by Christophe Cornut.

This page was built for publication: Sur le rang des courbes elliptiques sur les corps de classes de Hilbert