Pair correlation and twin primes revisited

Brian Conrey, Jon P Keating

Research output: Contribution to journalArticle (Academic Journal)peer-review

5 Citations (Scopus)
320 Downloads (Pure)


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.
Original languageEnglish
Article number20160548
Number of pages11
JournalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Issue number2194
Early online date5 Oct 2016
Publication statusPublished - Oct 2016


  • pair correlation
  • random matrix theory
  • twin primes


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