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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 quintic obstruction for a fixed-center Riemann theta product

Scott Schubr

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Abstract

We exhibit an explicit polynomial square on which the signed derivative functional of a fixed-center Riemann theta product is negative. At the center s_0=(1)/(4)log(13/(4π)), the polynomial P(X)=X^5-264X^3+10952X satisfies ℒ_(s_0)(P^2)≤-1 351 625 671. The certificate uses rational interval arithmetic for derivatives through order ten and an explicit bound on the complete infinite theta tail. It follows that the normalized product at this center is not positive definite and that its odd derivative Hankel block is indefinite.

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