## Abstract

Let π (respectively π0) be a unitary cuspidal automorphic representation of GLm (respectively GLm0 ) over Q. We prove log-free zero density estimates for Rankin-Selberg Lfunctions of the form L(s;π × π0), where π varies in a given family and π0 is fixed. These estimates are unconditional in many cases of interest; they hold in full generality assuming an average form of the generalized Ramanujan conjecture. We consider applications of these estimates related to mass equidistribution for Hecke-Maaß forms, the rarity of Landau-Siegel zeros of Rankin-Selberg L-functions, the Chebotarev density theorem, and torsion in class groups of number fields.

Original language | English |
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Pages (from-to) | 1471-1541 |

Number of pages | 71 |

Journal | Journal of the European Mathematical Society |

Volume | 24 |

Issue number | 5 |

DOIs | |

Publication status | Published - 2022 |

## Keywords

- automorphic form
- log-free zero density estimate
- Rankin-Selberg L-function