Congruent numbers with many prime factors

DOI10.1073/pnas.1216991109zbMath1298.11053arXiv1210.8231OpenAlexW2129322133WikidataQ36504286 ScholiaQ36504286MaRDI QIDQ4907500

Ye Tian

Publication date: 2 February 2013

Published in: Proceedings of the National Academy of Sciences (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1210.8231

zbMATH Keywords

congruent numbersHeegner point

Mathematics Subject Classification ID

Elliptic curves over global fields (11G05) (L)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture (11G40) Cubic and quartic Diophantine equations (11D25)

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Some new families of non-congruent numbers ⋮ Special automorphisms on Shimura curves and non-triviality of Heegner points ⋮ Congruent numbers, quadratic forms and \(K_2\) ⋮ 8-rank of the class group and isotropy index ⋮ Heegner points on modular curves ⋮ Congruent numbers ⋮ Quadratic twists of elliptic curves ⋮ On the weak forms of the 2-part of Birch and Swinnerton-Dyer conjecture ⋮ The Conjecture of Birch and Swinnerton-Dyer ⋮ Congruent numbers

Cites Work

• Mock Heegner points and congruent numbers
• A classical Diophantine problem and modular forms of weight \(3/2\)
• Diophantine analysis and modular forms
• Congruence Properties of Congruent Numbers