Pair correlation and twin primes revisited

© 2016 The Author(s) Published by the Royal Society. All rights reserved. We establish a connection between the conjectural two-over-two ratios formula for the Riemann zetafunction and a conjecture concerning correlations of a certain arithmetic function. Specifically, 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.