{"id":"hexagon/2610.00535","pdf":"https://hexagonmath.org/pdf/2610.00535v1","url":"https://hexagonmath.org/abs/2610.00535v1","tags":["msc:11M26","msc:15B05","msc:05E05","msc:30D15","msc:35K05","Riemann ξ-function; de Bruijn–Newman constant; heat flow"],"score":0,"title":"Coefficient Dynamics and Consecutive Toeplitz Minors for the de Bruijn–Newman Famil","domain":"math.NT","source":"hexagon","authors":["Changxia Lin"],"reviews":0,"subject":"math.NT","summary":"Abstract We give a normalization-consistent coefficient formulation of the de Bruijn–Newman heat flow attached to the Riemann ξ-function. For the classical kernel Φ and the family Ht(z) = Z ∞ 0 e tu2 Φ(u) cos(zu) du, Ft(w) = Ht(i √ w) = X n≥0 qn(t)w n , we prove the exact evolution laws ∂tFt = 2F ′ t + 4wF′′ t , q(m) n (t) = (2n + 2m)! (2n)! qn+m(t). The coefficients have positive integral representations and the transformed entire function has order at most 1/2. We relate the zeros of Ft to the Pólya–frequency property of (qn(t)), derive the rectangular Jacobi–Trudi identity for the…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-10-26","reactions":{},"withdrawn":false,"authorship":"human","formalized":false,"human_understanding":"all"}