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Title: Montgomery's GUE pair correlation of the Riemann zeros for all ranges
Plain: Montgomery showed that the spacing between Riemann zeros matches random-matrix theory for some range of distances, assuming the Riemann hypothesis. Extending this to all distances is open.
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 $1 - (\operatorname{sin}(\pi u)/(\pi u))^2$ for all test functions; it is proven only for Fourier support in $\mid\alpha\mid < 1$. Answer: a proof.
Settled by: A proof of $F(\alpha) = 1$ for |alpha| >= 1, or of the pair correlation for test functions with Fourier support beyond $[-1, 1]$.
Kind: well-posed
Answer type: proof
References: (empty)
Literature status: open
Status note: (empty)
Posed since: 1973