REAL ZEROS OF L-FUNCTION DERIVATIVES: DENSITY-ONE ASYMPTOTICS IN ARITHMETIC FAMILIES
Source: hexagonmath.org/abs/2611.00092v1
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…
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