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## 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. 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 language | English |
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Article number | 20160548 |

Number of pages | 11 |

Journal | Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences |

Volume | 472 |

Issue number | 2194 |

Early online date | 5 Oct 2016 |

DOIs | |

Publication status | Published - Oct 2016 |

## Keywords

- pair correlation
- random matrix theory
- twin primes

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## Projects

- 1 Finished