A refined version of the Siegel-Shidlovskii theorem

Details A refined version of the Siegel-Shidlovskii theorem A refined version of the Siegel-Shidlovskii theorem

2004-05-28

arxiv.org/abs/math/0405549v3

Mathematics

Number Theory

9 pages 2nd version: Changed title, added reference to D.Bertrand and corrected error in definition of H in the proof of Theor

Scientific paper

Using Y.Andr\'e's result on differential equations staisfied by
$E$-functions, we derive an improved version of the Siegel-Shidlovskii theorem.
It gives a complete characterisation of algebraic relations over the algebraic
numbers between values of $E$-functions at any non-zero algebraic point.

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