Gel'fond-Schneider theorem

In mathematics, the Gel'fond-Schneider theorem is the following statement, originally proved by Aleksandr Gelfond :

α

is an algebraic number (with $\alpha\neq 0$ and $\alpha\neq 1$ ), and

β

α β

This statement implies that $2^{\sqrt{2}}$ (the Gelfond-Schneider constant) and $\sqrt{2}^{\sqrt{2}}$ (see nonconstructive proof) are transcendental numbers.

The Gelfond-Schneider theorem is a partial answer to Hilbert's seventh problem.

Last updated: 05-24-2005 07:10:00

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