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On the assumption of the Riemann hypothesis, we show that over a class ofsufficiently smooth test functions, a measure conjectured by Bogomolny andKeating coincides to a very small error with the actual pair correlationmeasure for zeroes of the Riemann zeta function. Our result extends the wellknown result of Montgomery that over the same class of test functions the paircorrelation measure coincides (to a larger error term) with that of theGaussian Unitary Ensemble (GUE). The restriction of test functions remainsstringent, but we are nonetheless able to detect, at a microscopically blurredresolution, macroscopic troughs in the pair correlation measure.

Macroscopic pair correlation of the Riemann zeroes for smooth test functions