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## Abstract

In upcoming papers by Conrey, Farmer and Zirnbauer there appear conjectural formulas for averages, over a family, of ratios of shifted

*L*-functions. In this paper we will present various applications of these ratios conjectures to a wide variety of problems that are of interest in number theory, such as lower order terms in the zero statistics of*L*-functions, mollified moments of*L*-functions and discrete averages over zeros of the Riemann zeta functions. In particular, using the ratios conjectures we easily derive the answers to a number of notoriously difficult computations.Translated title of the contribution | Applications of the L-functions ratios conjecture |
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Original language | English |

Pages (from-to) | 594 - 646 |

Number of pages | 53 |

Journal | Proceedings of the London Mathematical Society |

Volume | 94 (3) |

DOIs | |

Publication status | Published - May 2007 |

### Bibliographical note

Publisher: Oxford University Press## Fingerprint Dive into the research topics of 'Applications of the <i>L</i>-functions ratios conjecture'. Together they form a unique fingerprint.

## Projects

- 1 Finished