63 citations · 557 across the 46 of their papers we have counts for
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math.NT2017★ 12 cited
Three-isogeny Selmer groups and ranks of abelian varieties in quadratic twist families over a number field
Manjul Bhargava, Zev Klagsbrun, Robert J. Lemke Oliver +1
For an abelian variety over a number field , we prove that the average rank of the quadratic twists of is bounded, under the assumption that the multiplication-by-3 isog…
math.NT2017★ 13 cited
Bounds on 2-torsion in class groups of number fields and integral points on elliptic curves
Manjul Bhargava, Arul Shankar, Takashi Taniguchi +3
We prove the first known nontrivial bounds on the sizes of the 2-torsion subgroups of the class groups of cubic and higher degree number fields (the trivial bound being $O_ε(|{…