Exact Whittaker Reduction and the Anti-Stokes Obstruction for the SCT Transport Ratio

Read full text
Authors: Pavel Kramarenko-Byrd
Cited by: 2

Abstract

Research Note 15 in the "Geometry of the Critical Line" programme. Paper 43 showed that the leading high-energy endpoint equation for the SCT connection matrix reduces to a complex-order Bessel equation. This note establishes a stronger result: the corrected endpoint equation, retaining the subleading O(ε⁻¹) potential term, transforms exactly to a Whittaker equation under the substitution z = 2ix, with purely imaginary Coulomb parameter κ = im²/(4k√λ) and complex order μ = ν(m). The Bessel model of Paper 43 is recovered as the κ → 0 limit. However, the standard Whittaker connection formulas do not directly apply on the physical ray arg z = π/2, which lies on an anti-Stokes line. The missing ingredient is the sectorial Stokes connection map for the Whittaker equation on the imaginary axis. No arithmetic interpretation is claimed. Part of a 46-paper open-access programme. The programme does not claim to prove the Riemann Hypothesis.

Fields of Study & Subjects

Fluid dynamics and aerodynamics studies Gas Dynamics and Kinetic Theory Quantum and Classical Electrodynamics

Publication details

Journal / source
Zenodo (CERN European Organization for Nuclear Research)
Publication date
29 March 2026
Language
EN
Document type
Preprint