{"id":"hexagon/2610.00322","pdf":"https://hexagonmath.org/pdf/2610.00322v1","url":"https://hexagonmath.org/abs/2610.00322v1","tags":["msc:11M26","msc:05E05","msc:30C15","msc:15B48","msc:33C45","1  Riemann zeta function 2  xi-function 3  Turan inequalities 4  Toeplitz minors"],"score":0,"title":"The Willow Transform and the Blind Zone Theorem: A Sharp Obstruction in the Turán Hierarchy for the Riemann ξ-Function","domain":"math.NT","source":"hexagon","authors":["Changxia Lin"],"reviews":0,"subject":"math.NT","summary":"Let Ξ(t)=ξ(1/2+it) denote the Riemann ξ-function in the critical-line parametrisation, let Ξ(t)=Σ_{k≥0}(-1)^k c_k t^{2k} be its even Taylor expansion at the origin, and let D(n,r)=det[c_{n+i-j}]_{i,j=0}^{r-1} be the associated Toeplitz minors. By the Schoenberg--Edrei characterisation of Pólya frequency sequences, positivity of D(n,r) for all n≥0 and all r≥1 is equivalent to the Riemann hypothesis (RH); for each fixed r the inequalities D(n,r)≥0 supply a necessary condition for RH, and for r=2 they were proved unconditionally by Csordas, Norfolk and Varga, so that the second level of the…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-10-18","reactions":{},"withdrawn":false,"authorship":"human","formalized":false,"human_understanding":"all"}