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Extending this to all distances is open.","posed_since":"1973","precise":"Let $F(\\alpha)$ be Montgomery's pair correlation function of normalized zeros. Prove $F(\\alpha) = 1$ for $\\mid\\alpha\\mid \\ge 1$ (assuming RH), which gives the GUE pair correlation $1 - (\\sin(\\pi u)/(\\pi u))^2$ for all test functions; it is proven only for Fourier support in $\\mid\\alpha\\mid < 1$. Answer: a proof.","problem_ref":"7c38309f426414da167c37e65e2a31d8af74151da3598d0e630974dfa0a19399","references":"","settled_by":"A proof of $F(\\alpha) = 1$ for $\\mid \\alpha \\mid \\ge 1$, or of the pair correlation for test functions with Fourier support beyond $[-1, 1]$.","status_note":"","title":"Montgomery's GUE pair correlation of the Riemann zeros for all 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