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  1. Uniform Resolvent Asymptotics for Growing Theta-Null Source FamiliesScott SchubrEdition 1 · 2026-10-27 Public
  2. Frequency-Source Resolvent Limits and Positive-Receiver InstabilityScott SchubrEdition 1 · 2026-10-27 Public
  3. Arithmetic cutoff bounds and sharp tail capacity for local Nyman–Beurling certificatesScott SchubrEdition 4 · 2026-10-27 Public
  4. An explicit hyperbolicity threshold for xi Jensen polynomialsScott SchubrEdition 2 · 2026-10-27 Public
  5. Collision-uniform kernel asymptotics for Báez–Duarte zero packetsScott SchubrEdition 3 · 2026-10-27 Public
  6. Sharp logarithmic sampling thresholds and lacunary interpolation in the Báez–Duarte step spaceScott SchubrEdition 2 · 2026-10-27 Public
  7. Polynomial cores and inertia under Carleman moment boundsScott SchubrEdition 2 · 2026-10-27 Public
  8. Finite-projection holomorphic stabilization of contractible affine hypersurfacesScott SchubrEdition 3 · 2026-10-27 Public
  9. Compact capture and protected bridges on the Koras–Russell cylinderScott SchubrEdition 2 · 2026-10-27 Public
  10. Dimension-dependent holomorphic certificate degrees on zero-sum hyperplanesScott SchubrEdition 2 · 2026-10-27 Public
  11. Admissible kernel lifts with positive endpoint forms and nonreal Fourier zerosScott SchubrEdition 2 · 2026-10-27 Public
  12. Global finite-depth stability and nonreal zeros of admissible Fourier transformsScott SchubrEdition 2 · 2026-10-27 Public
  13. Weighted polynomial localization and theta correction inertiaScott SchubrEdition 2 · 2026-10-27 Public
  14. Critical-tail localization and growing theta correction inertiaScott SchubrEdition 2 · 2026-10-27 Public
  15. Typical-value anchors for polynomial approximation and theta correction inertiaScott SchubrEdition 2 · 2026-10-27 Public
  16. All-depth root-Laguerre positivity with nonreal Fourier zerosScott SchubrEdition 3 · 2026-10-27 Public
  17. Polynomial synthesis and zero ideals for the Riemann xi-functionScott SchubrEdition 2 · 2026-10-27 Public
  18. A counterexample and corrected translation-density criterion for correlation kernelsScott SchubrEdition 2 · 2026-10-27 Public
  19. Finite theta interpolation and eventual Laguerre failureScott SchubrEdition 2 · 2026-10-27 Public
PublicEdition 2

An explicit hyperbolicity threshold for xi Jensen polynomials

Scott Schubr

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Abstract

We give an explicit sufficient shift for hyperbolicity of the degree-d Jensen polynomials attached to Riemann's xi-function. Every integer n≥max{65536,⌈16√(d+1)log(d+3)⌉} is sufficient. The estimate replaces the exponent loss in the qualitative O_ε(d^(1/2+ε)) threshold by a critical logarithmic factor and an effective onset. The proof quantitatively specializes the derivative-escape argument of Kim and Lee, using the classical zero strip, Gontcharoff interpolation, Cauchy's estimate and an elementary growth bound for xi. We also give a sharper scalar criterion and a portable exact checker for its rational enclosures.

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