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arXiv · 1204.0498

A Note on Schanuel's Conjectures for Exponential Logarithmic Power Series Fields

Salma Kuhlmann·Mickael Matusinski·Ahuva C. Shkop
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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.

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Salma Kuhlmann, Mickael Matusinski, Ahuva C. Shkop. 2012-04-02. A Note on Schanuel's Conjectures for Exponential Logarithmic Power Series Fields. https://doi.org/10.1007/s00013-013-0520-5

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