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- Manjul Bhargava, Jonathan Hanke
- 2011

Using maximal isotropic submodules in a quadratic module over Z p , we prove the existence of a natural discrete probability distribution on the set of isomorphism classes of short exact sequences of co-finite type Z p-modules, and then conjecture that as E varies over elliptic curves over a fixed global field k, the distribution of is that one. We show… (More)

- Manjul Bhargava, Wednesday
- 2015

Professor Bhargava's work on composition laws revolutionized algebraic number theory, and earned him the Cole Prize in number theory, the SASTRA Ramanujan Prize, and a Clay Research Award, as well as a full professorship at Princeton at the age of 29—just two years after earning his PhD. He is fascinated by mathematical patterns that arise in music and… (More)

- Jennifer Mun, Young Park, Bjorn Poonen, Matt Baker, Jennifer S Balakrishnan, Manjul Bhargava +30 others
- 2014

Faltings' theorem states that curves of genus g > 2 have finitely many rational points. Using the ideas of Faltings, Mumford, Parshin and Raynaud, one obtains an upper bound on the upper bound on the number of rational points [Szp85], XI, §2, but this bound is too large to be used in any reasonable sense. In 1985, Coleman showed [Col85] that Chabauty's… (More)

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