A note on Schanuel%26apos;s conjectures for exponential logarithmic power series fields

作者：Kuhlmann Salma^*; Matusinski Mickael; Shkop Ahuva C

来源：Archiv der Mathematik, 2013, 100(5): 431-436.

DOI：10.1007/s00013-013-0520-5

• Schanuel%26apos
• s conjectures
• Generalized series fields with derivation
• Exponential-logarithmic series fields with derivation

In Ax (Ann. Math. 93(2):252-268, 1971), J. Ax proved a transcendency theorem for certain differential fields of characteristic zero : the differential counterpart of the still open Schanuel conjecture about the exponential function over (Lang, Introduction to transcendental numbers, 1966). In this article, we derive from Ax%26apos;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.

• 出版日期2013-5