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Gel'fond-Schneider theorem
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In mathematics, the Gel'fond-Schneider theorem is the following statement, originally proved by Aleksandr Gelfond :
- If α is an algebraic number (with
and 
), and β is an irrational algebraic number, then αβ is a transcendental number.
This statement implies that 
(the Gelfond-Schneider constant) and 
(see nonconstructive proof) are transcendental numbers.
The Gelfond-Schneider theorem is a partial answer to Hilbert's seventh problem.
10-26-2009 08:16:03
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The contents of this article is licensed from www.wikipedia.org under the GNU Free Documentation License. Click here to see the transparent copy and copyright details