RIFFAUT, Antonin

doi:10.1142/S1793042119500234

Métadonnées

Afficher la notice complète

Licence d’utilisation du document

RIFFAUT, Antonin
Institut de Mathématiques de Bordeaux [IMB]
Lithe and fast algorithmic number theory [LFANT]

Langue

Article de revue

Ce document a été publié dans

International Journal of Number Theory. 2019, vol. 15, n° 3, p. 445-468

World Scientific Publishing

Résumé en anglais

We treat two different equations involving powers of singular moduli. On the one hand, we show that, with two possible (explicitly specified) exceptions, two distinct singular moduli j(τ), j(τ ′) such that the numbers 1, j(τ) m and j(τ ′) n are linearly dependent over Q for some positive integers m, n, must be of degree at most 2. This partially generalizes a result of Allombert, Bilu and Pizarro-Madariaga, who studied CM-points belonging to straight lines in C 2 defined over Q. On the other hand, we show that, with " obvious " exceptions, the product of any two powers of singular moduli cannot be a non-zero rational number. This generalizes a result of Bilu, Luca and Pizarro-Madariaga, who studied CM-points belonging to an hyperbola xy = A, where A ∈ Q.< Réduire

Mots clés en anglais

Singular modulus

Conjecture of André–Oort

Complex multiplication

Métadonnées

Partager cette publication !

Licence d’utilisation du document

Equations with powers of singular moduli

Langue

Ce document a été publié dans

Résumé en anglais

Mots clés en anglais

URI

DOI

Origine

Unités de recherche