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Publication - Professor Jon Keating

    Pair correlation and twin primes revisited


    Conrey, B & Keating, JP, 2016, ‘Pair correlation and twin primes revisited’. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol 472.


    We establish a connection between the conjectural two-over-two ratios formula for the Riemann zeta-function and a conjecture concerning correlations of a certain arithmetic function. Speci cally, we prove that the ratios conjecture and the arithmetic correlations conjecture imply the same result. This casts a new light on the underpinnings of the ratios conjecture, which previously had been motivated by analogy with formulae in random matrix theory and by a heuristic recipe.

    Full details in the University publications repository