X-unités de certains corps de fonctions algébriques. I. (X-units of some algebraic function fields. I). (French) Zbl 0584.12009

Paysant le Roux, Roger

Groupe Étude Théor. Anal. Nombres 1re/2e années: 1984/1985, Exp. No. 18, 7 p. (1985).

Let K be the field \({\mathbb{Q}}(X)\) of rational functions over the field \({\mathbb{Q}}\). The author considers units in certain subrings of cubic extensions of K, the corresponding norm equation being regarded as an analog of Pell’s equation.

Reviewer: E.-U.Gekeler

MSC:

11R58	Arithmetic theory of algebraic function fields
14H45	Special algebraic curves and curves of low genus
14H40	Jacobians, Prym varieties
11D57	Multiplicative and norm form equations

Keywords:

units in orders; rational functions; norm equation; Pell’s equation

Citations:

Zbl 0584.12010