16 citations · 48 across the 25 of their papers we have counts for
3 papers · 1 filter
The second moment of the size of the -Selmer group of elliptic curves
Manjul Bhargava, Arul Shankar, Ashvin Swaminathan
In this paper, we prove that when elliptic curves over are ordered by height, the second moment of the size of the -Selmer group is at most . This confirms a co…
Geometry-of-numbers methods in the cusp
Arul Shankar, Artane Siad, Ashvin Swaminathan +1
In this article, we develop new methods for counting integral orbits having bounded invariants that lie inside the cusps of fundamental domains for coregular representations. We il…
Hermite equivalence of polynomials
Manjul Bhargava, Jan-Hendrik Evertse, Kálmán Győry +2
In this paper, we resurrect a long-forgotten notion of equivalence for univariate polynomials with integral coefficients introduced by Hermite in the 1850s. We show that the Hermit…