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


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.


  • Henryk Żołądek

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