The effect of twisting on the 2-Selmer group
By P. Swinnerton-Dyer. Mathematical Proceedings of the Cambridge Philosophical Society, 2008
70 citations recorded by the source corpus.
Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/a4380515d897cb4b93890665eb9a8e140cc173f2
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Algebra and Number Theory
- Manjul Bhargava
- A. Shankar
- Daniel M. Kane
- Barry Mazur
- Karl Rubin
- Bjorn Poonen
- B. Gross
- Melanie Matchett Wood
In Geometry and Topology
- Manjul Bhargava
- A. Shankar
- Barry Mazur
- Daniel M. Kane
- Karl Rubin
- Bjorn Poonen
- B. Gross
- Melanie Matchett Wood
In Mathematical Physics
- A. Shankar
- Manjul Bhargava
- Barry Mazur
- Daniel M. Kane
- Karl Rubin
- Melanie Matchett Wood
- Akshay Venkatesh
- B. Gross
Citations in the corpus
- On the ranks of the 2-Selmer groups of twists of a given elliptic curve (2010, methodology): “Then the main theorem of [Swinnerton-Dyer 2008] together with Lemma 1 implies: Theorem 2.”
- Ranks of twists of elliptic curves and Hilbert’s tenth problem (2009, result): “Related results have been obtained by Swinnerton-Dyer [27] when K = Q and E is an elliptic curve with all 2-torsion points rational.”
- Binary quartic forms having bounded invariants, and the boundedness of the average rank of elliptic curves (2010, background): “This connection between 2-Selmer group elements and binary quartic forms was first introduced and used in the original elliptic curve computations of Birch and Swinnerton-Dyer, which led them to their celebrated conjecture.”