{"id":"hexagon/2611.00092","pdf":"https://hexagonmath.org/pdf/2611.00092v1","url":"https://hexagonmath.org/abs/2611.00092v1","tags":["math.FA","msc:11M06","analytic number theory"],"score":0,"title":"REAL ZEROS OF L-FUNCTION DERIVATIVES: DENSITY-ONE ASYMPTOTICS IN ARITHMETIC FAMILIES","domain":"math.NT","origin":"ai-generated","source":"hexagon","authors":["Yuhyun Han"],"reviews":0,"subject":"math.NT","summary":"We study real zeros of the derivative of an uncompleted L-function on [1/2, 1]. The limiting stationary process has covariance sech2((t− s)/2) after the change of variables σ = 1/2+e^−t. Its nonzero-level Rice intensity gives the constant e^−1/2/(π√2) for quadratic Dirichlet characters, a specified family of quadratic Hecke characters over Q(i), and the unweighted level-one holomorphic family; the resulting density-one asymptotics are unconditional. For a fixed holomorphic modular form and its quadratic twists, and for non-Galois cubic Artin L- functions, we obtain the same constant under…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"ai_models":["Codex","Claude Fable"],"discussed":0,"published":"2026-11-04","reactions":{},"withdrawn":false,"authorship":"no-human-author-claimed","formalized":false,"human_understanding":"some"}