Asymptotic Evans Zero Law for the Chiral SCT Operator

Read full text
Authors: Pavel Kramarenko-Byrd
Cited by: 10

Abstract

Paper 46 in the "Geometry of the Critical Line" programme. This paper derives the leading asymptotic law for the Evans zeros of the connection-matrix entry M₂₁(λ,m) of the chiral SCT operator. The proof uses exact Liouville reduction (the identity B = −A'/2), endpoint Laurent analysis, and complex-order Bessel matching. The Evans numerator reduces to sinh(β + iα), where β = Im(ν)π and α = Φ_tot − Re(ν)π − π/2. The main results at leading asymptotic order: (i) the leading asymptotic Evans model has no real zeros for m ≠ 0; (ii) the zeros satisfy Δ√(Re λₙ) → π/L with L = 2/k; (iii) for m > 0 the zeros lie in Im(λ) < 0 with depth D_m = π|Im(r₁−r₂)|/L, where r₁, r₂ are the Frobenius exponents at the right endpoint; (iv) for m < 0 the zeros lie in Im(λ) > 0 by chiral conjugation. Numerical verification in the m = 2 and m = 4 sectors confirms the predicted depth to within 1% and 4% respectively, with the discrepancy consistent with finite-λ convergence. Subleading corrections are not computed here. The lower-half-plane location is a leading-order result, not yet a full non-perturbative theorem. No arithmetic interpretation is claimed. Part of a 46-paper open-access programme on the geometry of the Riemann zeta function's critical line, anchored by the SCT 5-Manifold and the cover equation Φ + e^{iπ − 1/Φ} = 0.

Fields of Study & Subjects

Mathematical functions and polynomials Matrix Theory and Algorithms Quantum Chromodynamics and Particle Interactions

Publication details

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