Two remarks about Picard-Vessiot extensions and elementary functions

Volume 84 / 2000

Henryk Żołądek Colloquium Mathematicum 84 (2000), 173-183 DOI: 10.4064/cm-84/85-1-173-183

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 $Gal_{L} M$ is a normal subgroup of $Gal_{K} M$. We also present a proof that the probability function Erf(x) is not an elementary function.

Authors

  • Henryk Żołądek

Search for IMPAN publications

Query phrase too short. Type at least 4 characters.

Rewrite code from the image

Reload image

Reload image