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We establish a connection between the ratios conjecture for the Riemannzeta-function and a conjecture concerning correlations of convolutions ofM\"{o}bius and divisor functions. Specifically, we prove that the ratiosconjecture and an arithmetic correlations conjecture imply the same result.This provides new support for the ratios conjecture, which previously had beenmotivated by analogy with formulae in random matrix theory and by a heuristicrecipe. Our main theorem generalises a recent calculation pertaining to thespecial case of two-over-two ratios.

Averages of ratios of the Riemann zeta-function and correlations of divisor sums