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Title

Two remarks about Picard-Vessiot extensions and elementary functions

Authors 1

Affiliations

  1. Institute of Mathematics, University of Warsaw, Banacha 2, 02-097 Warszawa, Poland

Abstract

We present a simple proof of the theorem which says that for a series of extensions of differential fields K ⊂ L ⊂ M, where K ⊂ M is Picard-Vessiot, the extension K ⊂ L is Picard-Vessiot iff the differential Galois group GalLM is a normal subgroup of GalKM. We also present a proof that the probability function Erf(x) is not an elementary function.

Bibliography

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Colloquium Mathematicum
2000/84/85/1
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Pages:
173-183
Main language of publication
English
Received
1999-06-11
Accepted
1999-10-01
Published
2000
Exact and natural sciences