Locating Quintic Obstructions in the Riemann Theta Product: A certified transition and minimum-degree theorem
Loading original first page…
Abstract
We give a reproducible method for locating and certifying quintic obstructions for the normalized fixed-center Riemann theta product, and prove a unique transition in its odd quintic moment block on [3.64,3.66]. The transition parameter lies strictly between 3.64888758188562 and 3.64888758188563. For x∈ I=[3.64,3.66], below the transition, degree five is the minimum degree of a polynomial whose square has negative signed-moment value; at the transition the degree-five form is positive semidefinite with a one-dimensional nullspace; above it the form is positive definite. The proof combines a Schur-complement reduction with uniform directed interval bounds, including the complete infinite theta tails. An exact rational arithmetic replay verifies the bounds on the entire interval. An explicit integer-coefficient quintic illustrates why testing one fixed polynomial does not locate the transition of the full quintic block.
Read the full paper in the original PDF.
Edition files
- Locating_Quintic_Obstructions_Transition_and_Minimum_Degree.pdf85.0 KiB · pdf
SHA-256
ff29f70507305638153ee7c3ce39e9ae3af41a8cc72873ce2ec076b5f186e888 - Revised_publication_package.zip1730.8 KiB · package
SHA-256
102f7902e8cbb77d70e54116abd2dfc5ccb33f024c940cc39a6e25c7b9b15016
Available editions
Research details
- Subjects
- Mathematics · Number Theory and Special Functions
- Keywords
- Riemann theta density, moment matrices, positive definiteness, quintic obstruction, computer-assisted proof
- Manuscript date
- 2026-10-18
- Reader reuse
- No additional permission granted
Scope
A unique certified odd-quintic transition on [3.64,3.66], exact minimum degree five below it and full degree-five positivity classification at and above it within that interval, with complete infinite theta tails.
Disclosures
AI assisted derivation, verification code, and preparation; the author takes responsibility for the manuscript.
Reproduction
The paper has 6 pages. The editable-source archive contains 19 files. Compile main.tex. Standard-library supplement/reproduce_all.py regenerates the interval and rational certificates in a new work directory; supplement/locate_quintic.py supports additional fixed-center witnesses.