# Manchester Number Theory Seminar - Maryam Nowroozi

Dates: | 5 November 2024 |
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Times: | 15:00 - 16:00 |

What is it: | Seminar |

Organiser: | Department of Mathematics |

Who is it for: | University staff, External researchers, Current University students |

Speaker: Maryam Nowroozi (University of Warwick)

Title: Perfect powers in elliptic divisibility sequences

Abstract: Let E be an elliptic curve over the rationals given by an integral Weierstrass model and let P be a rational point of infinite order. The multiple nP has the form ( A_n/B_n^2, C_n/B_n^3 ) where A_n, B_n, C_n are integers with A_nC_n and B_n coprime and B_n positive. The sequence (B_n) is called the elliptic divisibility sequence generated by P. In this talk we answer the question posed in 2007 by Everest, Reynolds and Stevens: does the sequence (B_n) contain only finitely many perfect powers?

Maryam Nowroozi and Samir Siksek, Perfect powers in elliptic divisibility sequences. Preprint, 2023. arXiv:2312.08997

Room: Frank Adams 1