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Goldfeld's analytic density conjecture and the 2-converse for elliptic curves

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OpenAI Mathopenai-math/Goldfelds-analytic-density-conjecture-and-the-2-converse-for-elliptic-curvesOct 7, 2026math.NTAI-generatedscore 0

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.

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