Algebraic Geometry/Ordinary Differential Equations
Algebraic properties of a class of p-adic exponentials
Comptes Rendus. Mathématique, Volume 344 (2007) no. 3, pp. 187-190.

In this Note we give an algebraic construction of a class of p-adic exponentials of Artin–Hasse type which are convergent in the disk D(0,1). Moreover we have a control for the field of coefficients of power series that defines such functions. Such objects were used by Christol and Robba to calculate the irregularity of a rank 1 p-adic differential operator, under the restriction of spherical completeness for the field of coefficients, and recently by Pulita, in order to classify the same equations.

Dans cette Note nous donnons une construction algébrique d'une classe d'exponentielles p-adiques du type d'Artin–Hasse qui sont convergentes dans le disque D(0,1). Nous avons d'ailleurs un contrôle des coefficients de la série entière qui définit de telles fonctions. De tels objets ont été employés par Christol et Robba pour calculer l'irrégularité d'un opérateur différentiel p-adique d'ordre 1, sous la restriction que le champ des coefficients soit sphériquement complet, et récemment par Pulita, afin de classifier les mêmes équations.

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Accepted:
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DOI: 10.1016/j.crma.2006.12.001
Chinellato, Daniele 1

1 Dip. di Matematica, Via Trieste 63, 35121 Padova, Italy
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Chinellato, Daniele. Algebraic properties of a class of p-adic exponentials. Comptes Rendus. Mathématique, Volume 344 (2007) no. 3, pp. 187-190. doi : 10.1016/j.crma.2006.12.001. http://www.numdam.org/articles/10.1016/j.crma.2006.12.001/

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