Asymptotic Evans Zero Law for the Chiral SCT Operator
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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 by chiral conjugation. Numerical verification in the m = 2 and m = 4 sectors confirms the…
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Keywords
- Bessel function
- Interpretation (philosophy)
- Riemann hypothesis
- Operator (biology)
- Laurent series
- Zero (linguistics)
- Cover (algebra)
- Connection (principal bundle)
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