Interpolation of hypergeometric ratios in a global field of positive characteristic

Anderson, Greg W.

Annales de l'Institut Fourier, Tome 57 (2007) no. 5, pp. 1655-1687.

Pour chaque corps global de caractéristique non nulle, nous donnons de nombreux exemples de fonctions algébriques en deux variables qui possèdent des propriétés consistantes avec un raffinement de la conjecture de Stark conjecturé récemment par l’auteur. Tous les exemples sont des unités de Coleman. Nous obtenons nos résultats en étudiant les chtoucas de rang un dont le zéro et le pôle sont génériques, et ne sont donc associés avec aucun module de Drinfeld.

For each global field of positive characteristic we exhibit many examples of two-variable algebraic functions possessing properties consistent with a conjectural refinement of the Stark conjecture in the function field case recently proposed by the author. All the examples are Coleman units. We obtain our results by studying rank one shtukas in which both zero and pole are generic, i. e., shtukas not associated to any Drinfeld module.

Classification : 11R37, 11T99
Keywords: Shtuka, hypergeometric ratio, Coleman unit
Mot clés : chtouca, rapport hypergéométrique, unité de Coleman

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