Entire or rational maps with integer multipliers - Laboratoire de Mathématiques d'Orsay
Pré-Publication, Document De Travail Année : 2022

Entire or rational maps with integer multipliers

Résumé

Let $\mathcal{O}_{K}$ be the ring of integers of an imaginary quadratic field $K$. Recently, Ji and Xie proved that every rational map $f \colon \widehat{\mathbb{C}} \rightarrow \widehat{\mathbb{C}}$ of degree $d \geq 2$ whose multipliers all lie in $\mathcal{O}_{K}$ is a power map, a Chebyshev map or a Lattès map. Their proof relies on a result from non-Archimedean dynamics obtained by Rivera-Letelier. In the present note, we show that one can avoid using this result by considering a differential equation instead. Our proof of Ji and Xie's result also applies to the case of entire maps. Thus, we also show that every nonaffine entire map $f \colon \mathbb{C} \rightarrow \mathbb{C}$ whose multipliers all lie in $\mathcal{O}_{K}$ is a power map or a Chebyshev map.
Fichier principal
Vignette du fichier
2212.03661v2.pdf (153 Ko) Télécharger le fichier
Origine Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-04854826 , version 1 (23-12-2024)

Identifiants

Citer

Xavier Buff, Thomas Gauthier, Valentin Huguin, Jasmin Raissy. Entire or rational maps with integer multipliers. 2024. ⟨hal-04854826⟩
0 Consultations
0 Téléchargements

Altmetric

Partager

More