A note on Schanuel's conjectures for exponential logarithmic power series fields

Salma Kuhlmann, Mickaël Matusinski, Ahuva C. Shkop

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

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 ℂ (Lang, Introduction to transcendental numbers, 1966). 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.

Original languageEnglish
Pages (from-to)431-436
Number of pages6
JournalArchiv der Mathematik
Volume100
Issue number5
DOIs
StatePublished - 1 May 2013

Keywords

  • Exponential-logarithmic series fields with derivation
  • Generalized series fields with derivation
  • Schanuel's conjectures

ASJC Scopus subject areas

  • General Mathematics

Fingerprint

Dive into the research topics of 'A note on Schanuel's conjectures for exponential logarithmic power series fields'. Together they form a unique fingerprint.

Cite this