The congruent number problem and elliptic curves

DOI10.4171/icm2022/85OpenAlexW4389775313MaRDI QIDQ6119692

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Publication date: 24 March 2024

Published in: International Congress of Mathematicians (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.4171/icm2022/85

zbMATH Keywords

\(L\)-functionquadratic twistscongruent numbersSelmer groupBSD conjectureGoldfeld conjecture

Mathematics Subject Classification ID

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

Cites Work

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• On the ranks of the 2-Selmer groups of twists of a given elliptic curve
• Explicit Gross-Zagier and Waldspurger formulae
• Anticyclotomic Iwasawa theory of CM elliptic curves
• Modeling the distribution of ranks, Selmer groups, and Shafarevich-Tate groups of elliptic curves
• Mock Heegner points and congruent numbers
• A classical Diophantine problem and modular forms of weight \(3/2\)
• Heegner points and derivatives of \(L\)-series
• Points de Heegner et dérivées de fonctions L p-adiques. (Heegner points and derivatives of p-adic L-functions)
• The ``main conjectures of Iwasawa theory for imaginary quadratic fields
• On the conjecture of Birch and Swinnerton-Dyer
• The size of Selmer groups for the congruent number problem. II. With an appendix by P. Monsky.
• Genus periods, genus points and congruent number problem
• The Birch and Swinnerton-Dyer formula for elliptic curves of analytic rank one
• Modular elliptic curves and Fermat's Last Theorem
• The Rankin's \(L\)-function and Heegner points for general discriminants
• The \(p\)-adic Gross-Zagier formula for elliptic curves at supersingular primes
• Generalized Heegner cycles and \(p\)-adic Rankin \(L\)-series. With an appendix by Brian Conrad
• The even parity Goldfeld conjecture: congruent number elliptic curves
• Selmer groups and the indivisibility of Heegner points
• Horizontal non-vanishing of Heegner points and toric periods
• A converse to a theorem of Gross, Zagier, and Kolyvagin
• \(p\)-converse to a theorem of Gross-Zagier, Kolyvagin and Rubin
• A \(p\)-adic Waldspurger formula
• The Iwasawa Main Conjectures for \(\mathrm{GL}_{2}\)
• Congruent numbers and Heegner points
• Diophantine analysis and modular forms
• On the -invariant of the cyclotomic derivative of a Katzp-adic -function
• Cube sum problem and an explicit Gross-Zagier formula
• Eisenstein congruence on unitary groups and Iwasawa main conjectures for CM fields
• The effect of twisting on the 2-Selmer group
• The Gross-Zagier Formula on Shimura Curves
• Anti-cyclotomic Katz $p$-adic $L$-functions and congruence modules
• The -adic Gross–Zagier formula on Shimura curves
• The Birch and Swinnerton-Dyer Conjecture: A brief survey

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