{"id":"openai-math/The-mean-analytic-rank-of-quadratic-twists-of-elliptic-curves","pdf":"https://github.com/openai/math/blob/main/preprints/The-mean-analytic-rank-of-quadratic-twists-of-elliptic-curves-October-6-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/The-mean-analytic-rank-of-quadratic-twists-of-elliptic-curves-October-6-2026","tags":["arithmetic-geometry","elliptic-curves","analytic-rank","l-functions"],"score":0,"title":"The mean analytic rank of quadratic twists of elliptic curves","domain":"Number theory","family":"006","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.NT","summary":"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.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-10-06","reactions":{},"formalized":false,"family_title":"Goldfeld’s conjecture: densities and mean analytic rank"}