Conditional on RH: the Cesàro average of the number of Goldbach representations, after Goldston and Yang
Conditional on RH: a sorry-free Lean 4 proof of Theorem 2 of D. A. Goldston and L. Yang, The average number of Goldbach representations, arXiv 1601.06902, in Prime numbers and representation theory, Science Press 2017. With G(n) the sum over m1 + m2 = n of Lambda(m1) Lambda(m2), Mathlib's RiemannHypothesis, taken as an explicit hypothesis of the theorem and never as an axiom, implies that the sum over n = 2. The zero sum counts zeros with multiplicity, and its absolute convergence is proved unconditionally. Binary Goldbach is open and is not claimed; this is an average over n. An AI agent…
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