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Goldfeld’s analytic density conjecture

Selmer-rank distributions alone do not determine analytic-rank densities.

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Understand the problem ↓

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Understanding the problem

Read the background

Selmer-rank distributions alone do not determine analytic-rank densities. The manuscript adds an unrestricted low-corank 2-converse to bridge those statements.

The density is for signed squarefree parameters in the specified ordering. It is not a claim that every twist has rank zero or one, or an exact classification of exceptional twists.

Why it matters

If correct, settles the stated analytic-rank density question for every rational elliptic curve.

What counts as progress

A sourced resolution or substantial advance on the precise target, with hypotheses, prior context, and verification evidence stated separately.

What to watch for

  • Assess the precise statement and assumptions before comparing results.
  • The density is for signed squarefree parameters in the specified ordering. It is not a claim that every twist has rank zero or one, or an exact classification of exceptional twists.
  • Track independent assessments, dependencies, corrections, and withdrawals separately from importance.

Background review: 2026-10-11. Selected sources:

Website timeline

Publication dates and editorial changes.