title: Pair correlation and twin primes revisited.
abstract: 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. 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.
authors.affiliation: American Institute of Mathematics, 600 East Brokaw Road, San Jose, CA 95112, USA; School of Mathematics, University of Bristol, Bristol BS8 1TW, UK.
authors.forename: Brian
authors.initials: B
authors.lastname: Conrey
authors.affiliation: School of Mathematics, University of Bristol , Bristol BS8 1TW, UK.
authors.forename: Jonathan P
authors.identifier: 0000-0003-0864-038X
authors.initials: JP
authors.lastname: Keating
keywords: pair correlation; random matrix theory; twin primes