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

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2013

Autor:innen

Mickaël, Matusinski
Shkop, Ahuva C.

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http://nbn-resolving.de/urn:nbn:de:bsz:352-263994
DOI (zitierfähiger Link)
https://doi.org/10.1007/s00013-013-0520-5
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Archiv der Mathematik. 2013, 100(5), pp. 431-436. ISSN 0003-889X. eISSN 1420-8938. Available under: doi: 10.1007/s00013-013-0520-5

Zusammenfassung

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.

Zusammenfassung in einer weiteren Sprache

Fachgebiet (DDC)
510 Mathematik

Schlagwörter

Primary 11J81, secondary 12H05, Schanuel's conjectures, generalized series fields with derivation, exponential-logarithmic series fields with derivation

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ISO 690KUHLMANN, Salma, Matusinski MICKAËL, Ahuva C. SHKOP, 2013. A note on Schanuel's conjectures for exponential logarithmic power series fields. In: Archiv der Mathematik. 2013, 100(5), pp. 431-436. ISSN 0003-889X. eISSN 1420-8938. Available under: doi: 10.1007/s00013-013-0520-5
BibTex
@article{Kuhlmann2013Schan-26399,
  year={2013},
  doi={10.1007/s00013-013-0520-5},
  title={A note on Schanuel's conjectures for exponential logarithmic power series fields},
  number={5},
  volume={100},
  issn={0003-889X},
  journal={Archiv der Mathematik},
  pages={431--436},
  author={Kuhlmann, Salma and Mickaël, Matusinski and Shkop, Ahuva C.}
}
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