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  1. Finite certificates for the lower edge of a weighted Weil operatorScott SchubrEdition 2 · 2026-10-27 Public
  2. Effective Prescribed-Gradient Stability for Homogeneous Real-Stable PolynomialsScott SchubrEdition 2 · 2026-10-27 Public
  3. Prescribed-gradient minimizers and coefficient stability for homogeneous real-stable polynomialsScott SchubrEdition 4 · 2026-10-27 Public
  4. Finite theta interpolation and eventual Laguerre failureScott SchubrEdition 2 · 2026-10-27 Public
  5. Uniform permanent-derivative compensation on the six-row conjugate-disjoint Gram locusScott SchubrEdition 2 · 2026-10-27 Public
  6. Certified complementary bounds for an odd Weil receiverScott SchubrEdition 1 · 2026-10-27 Public
  7. RH, Approximately: Certified Lower Bounds for Odd Weil PositivityScott SchubrEdition 1 · 2026-10-27 Public
  8. Sharp regularity criteria for arithmetic cutoff functionalsScott SchubrEdition 1 · 2026-10-26 Public
  9. Optimal energy for Dirichlet repairs in divisor bandsScott SchubrEdition 1 · 2026-10-26 Public
  10. Certified negative-band approximation for odd Weil formsScott SchubrEdition 1 · 2026-10-26 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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