Research Article · Preprint Mathematics
Admissible kernel lifts with positive endpoint forms and nonreal Fourier zeros
- Primary subject
- Mathematics
- Subject subfields
- Complex Analysis
- Paper type
- Research Article
- Manuscript stage
- Preprint
- Manuscript
- Archived
- Edition
- 1 · Permanent link
Overview
Abstract
We give a finite-atomic construction of admissible Fourier kernels with prescribed Fourier multipliers of positive finite atomic measures. A sufficiently broad hyperbolic-cosh base makes the translated mixture uniformly strictly log-concave while retaining an order-one entire Fourier transform. A global centered-moment and cumulant estimate also preserves strict concavity of G(u) = log φ(√u) and of log(S′(u)² − S(u)S″(u)), where S(u) = φ(√u). The required scales are explicit and conservative. An exact four-atom multiplier produces kernels satisfying these shape conditions whose physical endpoint moment matrices are positive definite at every finite order, while their Fourier transforms have nonreal zeros. All zeros can be confined to any prescribed horizontal strip; an interior physical parameter still has negative polynomial squares in both parities. Classical Turán consequences are stated with their coefficient normalization and do not imply real-zero closure. The construction strengthens a generic nonimplication within the full admissible class. It is not a counterexample to the Riemann theta kernel and does not resolve the Riemann hypothesis.
Keywords admissible Fourier kernels · Laguerre inequalities · log-concavity · entire functions · moment matrices · nonreal zeros
Scope of the work
Explicit finite-atomic global curvature and centered-cumulant lifting theorem, root-coordinate and second-level shape inequalities, and a fully admissible order-one counterexample to propagation from all endpoint moment orders to interior physical positivity. For each prescribed strip a different kernel is constructed. No actual Riemann-theta counterexample, RH resolution, optimal scale, minimum failure degree or worldwide-priority claim.
Reproduction notes
The complete 12-member package includes the 12-page PDF, seven editable TeX files, a Python standard-library exact checker, build instructions, citation metadata and SHA-256 manifest. An isolated rebuild reproduces all 12 page texts and geometry; normal and optimized checker outputs agree. Finite checks supplement the analytic proofs.
The manuscript
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Author disclosures
Research and manuscript preparation used AI assistance. This author preprint has not undergone external human refereeing. Classical Bessel, Laguerre, Turán and Jensen results and earlier author publications are credited in the manuscript.
A stable scholarly record
Cite this edition
Scott Schubr. (2026). Admissible kernel lifts with positive endpoint forms and nonreal Fourier zeros (Version 1). Luminary Research Archive. https://research.luminaryoddities.com/admissible-kernel-lifts-positive-endpoint-forms-nonreal-fourier-zeros/v/1
BibTeX
@techreport{luminary_admissible_kernel_lifts_positive_endpoint_forms_nonreal_fourier_zeros_v1,
title = {Admissible kernel lifts with positive endpoint forms and nonreal Fourier zeros},
author = {Scott Schubr},
year = {2026},
institution = {Luminary Research Archive},
type = {Research Article},
note = {Version 1},
url = {https://research.luminaryoddities.com/admissible-kernel-lifts-positive-endpoint-forms-nonreal-fourier-zeros/v/1}
}Loading discussion…