A. Shnidman

activity

20122026

most citedThe average size of the 3-isogeny Selmer groups of elliptic curves

y^{2} = x^{3} + k

23 citations · 108 across the 30 of their papers we have counts for

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math.NT2022★ 4 cited

Integers expressible as the sum of two rational cubes

Levent Alpöge, Manjul Bhargava, Ari Shnidman

We prove that a positive proportion of integers are expressible as the sum of two rational cubes, and a positive proportion are not so expressible, thus proving a conjecture of Dav…

math.NT2022

Arbitrarily large $p$ -torsion in Tate-Shafarevich groups

E. Victor Flynn, Ari Shnidman

We show that, for any prime $p$ , there exist absolutely simple abelian varieties over $Q$ with arbitrarily large $p$ -torsion in their Tate-Shafarevich group. To prove this…

Integers expressible as the sum of two rational cubes

Arbitrarily large p-torsion in Tate-Shafarevich groups

Arbitrarily large $p$ -torsion in Tate-Shafarevich groups