Families of polynomials of every degree with no rational preperiodic points

Warning The system is temporarily closed to updates for reporting purpose.

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)

Full text not available from this repository. (Request a copy)

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
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

Actions (login required)

View Item
View Item