The Riemann hypothesis is equivalent to an asymptotic for the average number of Goldbach representations, after Granville 2007
A sorry-free Lean 4 proof of Theorem 1A of A. Granville, Refinements of Goldbach's conjecture, and the generalized Riemann hypothesis, Funct. Approx. Comment. Math. 37 (2007): with G(n) the sum over m1 + m2 = n of Lambda(m1) Lambda(m2), Mathlib's RiemannHypothesis holds if and only if the sum of G(n) over n 0. Both directions are proved with no hypothesis: RH implies the asymptotic through the von Koch bound for psi(x) - x, and the asymptotic implies RH by the route reconstructed in part by Bhowmik, Halupczok, Matsumoto, Suzuki (arXiv 1704.06103) and completed by Bhowmik and Ruzsa (arXiv…
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