27 citations · 86 across the 16 of their papers we have counts for
6 papers · 1 filter
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…
On a local invariant of elliptic curves with a p-isogeny
Matthew Gealy, Zev Klagsbrun
An elliptic curve defined over a -adic field with a -isogeny comes equipped with an invariant that measures the valuation of the l…
Statistics of -groups modulo for the ring of integers of a varying quadratic number field
Bruce W. Jordan, Zev Klagsbrun, Bjorn Poonen +2
For each odd prime , we conjecture the distribution of the -torsion subgroup of as ranges over real quadratic fields, or over imaginary quadratic…
On the Joint Distribution Of and in Quadratic Twist Families
Daniel Kane, Zev Klagsbrun
If is an elliptic curve with a point of order two, then work of Klagsbrun and Lemke Oliver shows that the distribution of $\dim_{\mathbb{F}_2}\mathrm{Sel}_ϕ(E^d/\mathbb{Q}) - \…
The average sizes of two-torsion subgroups in quotients of class groups of cubic fields
Zev Klagsbrun
We prove a generalization of a result of Bhargava regarding the average size as varies among cubic fields. For a fixed set of rational primes , we obtain…
Davenport-Heilbronn Theorems for Quotients of Class Groups
Zev Klagsbrun
We prove a generalization of the Davenport-Heilbronn theorem to quotients of ideal class groups of quadratic fields by the primes lying above a fixed set of rational primes . Ad…