On central L-values and the growth of the 3-part of the Tate–Shafarevich group

DOI10.1142/S1793042123500392WikidataQ114071734 ScholiaQ114071734MaRDI QIDQ5881024

Yukako Kezuka

Publication date: 9 March 2023

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

Full work available at URL: https://arxiv.org/abs/2110.05521

zbMATH Keywords

elliptic curves\(L\)-functioncomplex multiplicationTate-Shafarevich group

Mathematics Subject Classification ID

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

Uses Software

• Magma
• PARI/GP

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Density of rational points on isotrivial rational elliptic surfaces
• On the Birch-Swinnerton-Dyer quotients modulo squares
• Groupes de Selmer et corps cubiques. (Selmer group and cubic fields)
• Heegner points and derivatives of \(L\)-series
• The ``main conjectures of Iwasawa theory for imaginary quadratic fields
• On the conjecture of Birch and Swinnerton-Dyer
• The Magma algebra system. I: The user language
• Modular elliptic curves and Fermat's Last Theorem
• Ring-theoretic properties of certain Hecke algebras
• Tamagawa number divisibility of central \(L\)-values of twists of the Fermat elliptic curve
• The Diophantine equation \(ax^3+by^3+cz^3=0\)
• On the modularity of elliptic curves over 𝐐: Wild 3-adic exercises
• Algorithm for determining the type of a singular fiber in an elliptic pencil
• Arithmetic on Curves of Genus 1. IV. Proof of the Hauptvermutung.
• An explicit Gross–Zagier formula related to the Sylvester conjecture
• Notes on elliptic curves. II.
• The diophantine equation X3 + Y3 = DZ3 and the conjectures of Birch and Swinnerton-Dyer.
• On Elliptic Curves with Complex Multiplication as Factors of the Jacobians of Modular Function Fields
• Arithmetic on Curves of genus 1. VI. The Tate-Safarevic group can be arbitrarily large.