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We formulate a conjecture on the convergence of the correlation energy series of the Liouville function. For every fixed integer h ≥ 1, let Sₕ (x) = Σ₍≤ₗ λ (n) λ (n+h) and Zₕ (3) = Σ₍=₁^∞ Sₕ (n) ²/n³. The Amparo LC Conjecture states that Zₕ (3) converges to a finite constant. We prove that this conjecture is strictly equivalent to Chowla's conjecture (1965) for k=2 (Universal Reduction Theorem). We establish an Inertia Lemma: if Zₕ (3) 0. Computational evidence with N = 200, 000 verifies convergence to 1. 3765, with 99. 97% of the series concentrated in n ≤ 10, 000. The convergence abscissa satisfies σc ≤ 0. 5. The conjecture reduces the 61-year-old Chowla problem to the finiteness of a single scalar.
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Germán Alonso Durango López (Sat,) studied this question.
www.synapsesocial.com/papers/6a13e8520e02ee3982d33076 — DOI: https://doi.org/10.5281/zenodo.20350416
Germán Alonso Durango López
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