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Publication - Professor Jon Keating

    Twin prime correlations from the pair correlation of Riemann zeros


    Keating, J & Smith, D, 2019, ‘Twin prime correlations from the pair correlation of Riemann zeros’. Journal of Physics A: Mathematical and Theoretical, vol 52.


    We establish, via a heuristic Fourier inversion calculation, that the Hardy-Littlewood twin prime conjecture is equivalent to an asymptotic formula for the two-point correlation function of Riemann zeros at a height E on the critical line. Previously it was known that the Hardy-Littlewood conjecture implies the pair correlation formula, and we show that the reverse implication also holds. An averaged form of the Hardy-Littlewood conjecture is obtained by inverting the E → ∞limit of the two-point correlation function and the precise form of the conjecture is found by including asymptotically lower order terms in the two-point correlation function formula.

    Full details in the University publications repository