A Note on Schanuel's Conjectures for Exponential Logarithmic Power Series Fields
Logic
2015-10-27 v3 Commutative Algebra
Abstract
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.
Keywords
Cite
@article{arxiv.1204.0498,
title = {A Note on Schanuel's Conjectures for Exponential Logarithmic Power Series Fields},
author = {Salma Kuhlmann and Mickael Matusinski and Ahuva C. Shkop},
journal= {arXiv preprint arXiv:1204.0498},
year = {2015}
}
Comments
6 pages, to appear in Archiv der Mathematik