Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 006-02. The mean analytic rank of quadratic twists of elliptic curves
Manuscript map · lines 2555–2564
OpenAI@2026-10-07#rem:oai-p-006-02
Authors: OpenAI. Family 006.
Title: The mean analytic rank of quadratic twists of elliptic curves.
Abstract: For every elliptic curve over ℚ, we prove that the average analytic rank of its quadratic twists tends to 1/2 when signed squarefree twist parameters are ordered by absolute value. This resolves Goldfeld's mean analytic-rank conjecture in this counting convention.
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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