Sadek, Mohammad
(2021)
*Families of polynomials of every degree with no rational preperiodic points.*
Comptes Rendus Mathematique, 359
(2).
pp. 195-197.
ISSN 1631-073X (Print) 1778-3569 (Online)

Official URL: https://dx.doi.org/10.5802/CRMATH.173

## Abstract

Let K be a number field. Given a polynomial f (x) ∈ K [x] of degree d ≥ 2, it is conjectured that the number of preperiodic points of f is bounded by a uniform bound that depends only on d and [K : Q]. However, the only examples of parametric families of polynomials with no preperiodic points are known when d is divisible by either 2 or 3 and K = Q. In this article, given any integer d ≥ 2, we display infinitely many parametric families of polynomials of the form ft (x) = xd +c(t), c(t) ∈ K (t), with no rational preperiodic points for any t ∈ K.

Item Type: | Article |
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Divisions: | Faculty of Engineering and Natural Sciences > Basic Sciences > Mathematics Faculty of Engineering and Natural Sciences |

Depositing User: | Mohammad Sadek |

Date Deposited: | 17 Aug 2022 13:48 |

Last Modified: | 17 Aug 2022 13:48 |

URI: | https://research.sabanciuniv.edu/id/eprint/43346 |