TY - JOUR
T1 - A note on Schanuel's conjectures for exponential logarithmic power series fields
AU - Kuhlmann, Salma
AU - Matusinski, Mickaël
AU - Shkop, Ahuva C.
N1 - Funding Information:
This joint work was inspired during the first author’s visit to Ben Gurion University sponsored by the Institute for Advanced Studies in mathematics at Ben Gurion University. The first author wishes to thank the institute for this opportunity. The third author was supported by a postdoctoral fellowship funded by the Skirball Foundation via the Center for Advanced Studies in Mathematics at Ben-Gurion University of the Negev.
PY - 2013/5/1
Y1 - 2013/5/1
N2 - 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.
AB - 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.
KW - Exponential-logarithmic series fields with derivation
KW - Generalized series fields with derivation
KW - Schanuel's conjectures
UR - http://www.scopus.com/inward/record.url?scp=84878384258&partnerID=8YFLogxK
U2 - 10.1007/s00013-013-0520-5
DO - 10.1007/s00013-013-0520-5
M3 - Article
AN - SCOPUS:84878384258
SN - 0003-889X
VL - 100
SP - 431
EP - 436
JO - Archiv der Mathematik
JF - Archiv der Mathematik
IS - 5
ER -