# A refined version of the Siegel–Shidlovskii theorem

### Abstract

Using Y. André’s result on differential equations satisfied 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 nonzero algebraic point.

## Authors

Frits Beukers

Mathematisch Instituut, Universiteit Utrecht, 3508 Utrecht, Netherlands