Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 006-01. Goldfeld's analytic density conjecture and the 2-converse for elliptic curves
Manuscript map · lines 2545–2554
OpenAI@2026-10-07#rem:oai-p-006-01
Authors: OpenAI. Family 006.
Title: Goldfeld's analytic density conjecture and the 2-converse for elliptic curves.
Abstract: We prove Goldfeld's analytic density conjecture: for every elliptic curve E over ℚ, the quadratic twists of E with analytic rank zero and one each have density 1/2 among signed squarefree twist parameters ordered by absolute value. We also prove the low-corank 2-converse: if the $2{}{}infty$-Selmer corank of E is zero or one, then it equals the analytic and Mordell–Weil ranks, and the Tate–Shafarevich group is finite.
This abstract is a catalogue record. It is not a verification and not a premise. It does not close O.1. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted.
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