MOMENTS OF THE ORDERS OF TATE–SHAFAREVICH GROUPS

DOI10.1142/S1793042105000133zbMath1082.11042MaRDI QIDQ5697214

Christophe Delaunay

Publication date: 17 October 2005

Published in: International Journal of Number Theory (Search for Journal in Brave)

zbMATH Keywords

elliptic curvesTate-Shafarevich groupCohen-Lenstra heuristicsL-series

Mathematics Subject Classification ID

Elliptic curves over global fields (11G05) (L)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture (11G40)

Related Items (max. 100)

ON SELMER GROUPS AND TATE–SHAFAREVICH GROUPS FOR ELLIPTIC CURVESy²=x³−n³ ⋮ Moments and distribution of central \(L\)-values of quadratic twists of elliptic curves ⋮ Orders of Tate-Shafarevich groups for the Neumann-Setzer type elliptic curves ⋮ A probabilistic model for the distribution of ranks of elliptic curves over \(\mathbb{Q}\) ⋮ Distribution of Selmer groups of quadratic twists of a family of elliptic curves ⋮ Height of rational points on quadratic twists of a given elliptic curve ⋮ Orders of Tate–Shafarevich groups for the cubic twists of $X_0(27)$ ⋮ Regulators of rank one quadratic twists ⋮ On elliptic curves and random matrix theory ⋮ A heuristic for boundedness of ranks of elliptic curves ⋮ Behaviour of the Order of Tate–Shafarevich Groups for the Quadratic Twists of $$X_0(49)$$

Cites Work

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• Mean values of derivatives of modular \(L\)-series
• The size of Selmer groups for the congruent number problem. II. With an appendix by P. Monsky.
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• Ring-theoretic properties of certain Hecke algebras
• On the modularity of elliptic curves over 𝐐: Wild 3-adic exercises
• Heuristics on Tate-Shafarevitch Groups of Elliptic Curves Defined over Q
• Sur une application de la formule de Selberg–Delange
• Integral moments of L-functions
• Random matrix theory and \(L\)-functions at \(s=1/2\).

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