## Abstract

Assuming the generalized Riemann hypothesis, we show using the asymptotic large sieve that 91% of the zeros of primitive Dirichlet L-functions are simple. This improves on earlier work of Özlük which gives a proportion of at most 86%. We further compute the q-analogue of the Pair Correlation Function F(α) averaged over all primitive Dirichlet L-functions in the range |α| < 2. Previously such a result was available only when the average included all the characters χ. As a corollary of our results, we obtain an asymptotic formula for a sum over characters similar to the one encountered in the Barban-Davenport-Halberstam Theorem.

Original language | English (US) |
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Pages (from-to) | 63-87 |

Number of pages | 25 |

Journal | Quarterly Journal of Mathematics |

Volume | 65 |

Issue number | 1 |

DOIs | |

State | Published - Mar 2014 |

## ASJC Scopus subject areas

- General Mathematics