Theorem of Gelfond-Schneider

In Mathematical, the theorem of Gelfond-Schneider , shown originally by Aleksandr Gelfond, is stated in the following way:

If $\backslash \; alpha\; \backslash ,$ is a algebraic Nombre different from 0 and 1 and if $\backslash \; beta\; \backslash ,$ is an algebraic number irrational then $\backslash \; alpha^\; \{\backslash \; beta\}\; \backslash ,$ is a transcendent Nombre.

This statement implies that $2^\; \{\backslash \; sqrt\; \{2\}\}$ (the Constante of Gelfond-Schneider) is a transcendent number like $\backslash \; sqrt\; \{2\}\; ^\; \{\backslash \; sqrt\; \{2\}\}$.

The theorem of Gelfond-Schneider is an answer partial to the 7th problem of Hilbert.

See too

• Theorem of Baker

External bond

• a text of Edouard Oudet

Category: Approximation diophantienne

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