$2^\infty$-Selmer groups, $2^\infty$-class groups, and Goldfeld's conjecture
Number Theory
2017-06-08 v2
Abstract
We prove that the -class groups of the imaginary quadratic fields have the distribution predicted by the Cohen-Lenstra heuristic. Given an elliptic curve E/Q with full rational 2-torsion and no rational cyclic subgroup of order four, we analogously prove that the -Selmer groups of the quadratic twists of E have distribution as predicted by Delaunay's heuristic. In particular, among the twists E^d with |d| < N, the number of curves with rank at least two is .
Keywords
Cite
@article{arxiv.1702.02325,
title = {$2^\infty$-Selmer groups, $2^\infty$-class groups, and Goldfeld's conjecture},
author = {Alexander Smith},
journal= {arXiv preprint arXiv:1702.02325},
year = {2017}
}
Comments
84 pages, comments welcome