A Note on Schanuel's Conjectures for Exponential Logarithmic Power Series Fields
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en
Article de revue
Ce document a été publié dans
Archiv der Mathematik. 2013, vol. 100, n° 5, p. 431-436
Springer Verlag
Résumé en anglais
In [1], J. Ax proved a transcendency theorem for certain differential fields of characteristic zero: the differential counterpart of the still open Schanuel's conjecture about the exponential function over the field of ...Lire la suite >
In [1], J. Ax proved a transcendency theorem for certain differential fields of characteristic zero: the differential counterpart of the still open Schanuel's conjecture about the exponential function over the field of complex numbers [11, page 30]. In this article, we derive from Ax's theorem transcendency results in the context of differential valued exponential fields. In particular, we obtain results for exponential Hardy fields, Logarithmic-Exponential power series fields and Exponential-Logarithmic power series fields.< Réduire
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