Reference : Effective Kummer Theory for Elliptic Curves |

E-prints/Working papers : Already available on another site | |||

Physical, chemical, mathematical & earth Sciences : Mathematics | |||

http://hdl.handle.net/10993/43271 | |||

Effective Kummer Theory for Elliptic Curves | |

English | |

Lombardo, Davide [Università di Pisa > Dipartimento di Matematica] | |

Tronto, Sebastiano [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >] | |

Undated | |

No | |

[en] Elliptic curves ; Kummer Theory | |

[en] Let E be an elliptic curve defined over a number field K, let α ∈ E(K) be a point of infinite
order, and let N −1 α be the set of N -division points of α in E(K). We prove strong effective and uniform results for the degrees of the Kummer extensions [K(E[N ], N −1 α) : K(E[N ])]. When K = Q, and under a minimal (necessary) assumption on α, we show that the inequality [Q(E[N ], N −1 α) : Q(E[N ])] ≥ cN 2 holds with a constant c independent of both E and α. | |

http://hdl.handle.net/10993/43271 | |

https://arxiv.org/abs/1909.05376 |

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