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Research Article · Preprint Mathematics

A Positive Corner Limit for Inverse Half-Powers of Vámos Quartics

Scott Schubr

  • Mathematics
  • Analysis and Spectral Theory
Primary subject
Mathematics
Subject subfields
Analysis and Spectral Theory
Paper type
Research Article
Manuscript stage
Preprint
Manuscript
Archived
Edition
1 · Permanent link
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Overview

Abstract

For each fixed parameter 0 < λ ≤ 64/27, this paper determines an anisotropic corner limit of the inverse Laplace distribution of a stable Vámos quartic raised to the power −1/2. The limit is an explicit positive density with arcsine slope sections. Convergence holds jointly in all scaled variables, including the variable where the exact partial inverse has a logarithmic singularity. The proof uses a modified Bessel partial inverse, differentiation to remove logarithmic counterterms and quantitative estimates for inversion on growing frequency regions. It also determines the first correction in the same joint distribution topology. Positivity of the full inverse distribution is not assumed. The result does not establish positivity at a positive scale or justify restriction of the converging distributions to a graph.

Keywords Vámos quartics · inverse Laplace distributions · corner asymptotics · modified Bessel functions · hyperbolic polynomials

Scope of the work

Joint corner convergence and its first distributional correction for each fixed positive stable parameter. Finite-scale positivity, endpoint complete monotonicity, conditional graph restriction and uniform behavior as λ tends to zero remain outside the result.

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Author disclosures

Author-posted preprint. AI-assisted internal research and verification do not constitute external human peer review or proof-assistant formalization.

References and related publications

  1. M. F. Atiyah, R. Bott and L. Gårding, Lacunas for hyperbolic differential operators with constant coefficients I , Acta Math. 124 (1970), 109–189.
  2. Y. Baryshnikov and R. Pemantle, Asymptotics of multivariate sequences, part III: quadratic points, Adv. Math. 228 (2011), 3127–3206. arXiv:0810.4898, version 3.
  3. F. W. J. Olver et al., eds., NIST Digital Library of Mathematical Functions , §10.31 and §10.32, accessed October 23, 2026.
  4. S. Schubr, Sharp Stability and Geometric Classification of a Vámos Quartic Deformation , 2026, edition 1. Luminary Research Archive .
  5. A. D. Scott and A. D. Sokal, Complete monotonicity for inverse powers of some combinatorially defined polynomials, Acta Math. 213 (2014), 323–392. arXiv:1301.2449, expanded version 3.

A stable scholarly record

Cite this edition

Scott Schubr. (2026). A Positive Corner Limit for Inverse Half-Powers of Vámos Quartics (Version 1). Luminary Research Archive. https://research.luminaryoddities.com/positive-corner-limit-inverse-half-powers-vamos-quartics/v/1

BibTeX
@techreport{luminary_positive_corner_limit_inverse_half_powers_vamos_quartics_v1,
  title = {A Positive Corner Limit for Inverse Half-Powers of Vámos Quartics},
  author = {Scott Schubr},
  year = {2026},
  institution = {Luminary Research Archive},
  type = {Research Article},
  note = {Version 1},
  url = {https://research.luminaryoddities.com/positive-corner-limit-inverse-half-powers-vamos-quartics/v/1}
}

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