Soit K un corps équipé dʼun endomorphisme σ. Dans cette Note, nous utilisons la théorie de Galois aux différences pour donner un critère dʼindépendance algébrique pour les solutions de σ-équations du premier ordre. Ce résultat nous permet de caractériser les solutions hyperalgébriques de ces σ-équations lorsque K est muni dʼune dérivation Δ telle que
Let K be a field equipped with an endomorphism σ. In this Note, we use difference Galois theory to give an algebraic independence criterion for solutions of first order σ-equations. This result allows us to characterize the hyperalgebraic solutions of such σ-equations when K is endowed with a derivation Δ such that
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Pierre Nguyen 1
@article{CRMATH_2011__349_17-18_943_0, author = {Pierre Nguyen}, title = {Hypertranscendance de fonctions de {Mahler} du premier ordre}, journal = {Comptes Rendus. Math\'ematique}, pages = {943--946}, publisher = {Elsevier}, volume = {349}, number = {17-18}, year = {2011}, doi = {10.1016/j.crma.2011.08.021}, language = {fr}, }
Pierre Nguyen. Hypertranscendance de fonctions de Mahler du premier ordre. Comptes Rendus. Mathématique, Volume 349 (2011) no. 17-18, pp. 943-946. doi : 10.1016/j.crma.2011.08.021. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2011.08.021/
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