Asymptotic Shift Thresholds for Polya-Schur Multipliers and a Certified Lower Bound on the de Bruijn-Newman Constant of the Davenport-Heilbronn Function
Year: 2026
Type: preprint
Abstract: Classifies real entire Polya-Schur multipliers G(-d^2/dz^2) acting on the completed Davenport-Heilbronn function Xi_DH(z) into three asymptotic Stieltjes logarithmic-derivative regimes governed by the Bohr-Kronecker supremum sigma* = 1.120362498183325..., constructs tower-lacunary canonical products (R_1 = 16, R_k = 2^(2^(R_{k-1}))) showing that upper order rho(G) in (1/2, 1) fails without root-gap regularity, certifies via a 64-ball FLINT/Arb parametric Interval-Newton cover that Polya's hyperbolic sinc multiplier strictly separates global real-rootedness from the infinite-height Kronecker threshold (sigma* - 1/2 < 311/500 < h_global*(G_sinc)), and proves the unconditional strict two-sided bounds Lambda_zeta <= 1/5 < 1153/5000 < Lambda_DH < 2*(sigma* - 1/2)^2 = 0.769699258304...
Author: Missiaen, Thijs
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7225829619
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