Gelfond’s theorem

Let α and β be algebraic over , with β irrational and α not equal to 0 or 1. Then αβ is transcendental over .

This is perhaps the most useful result in determining whether a number is algebraic or transcendental.

The theorem is also known as the Gelfond-Schneider TheoremMathworldPlanetmath.

Title Gelfond’s theorem
Canonical name GelfondsTheorem
Date of creation 2013-03-22 13:24:31
Last modified on 2013-03-22 13:24:31
Owner mathcam (2727)
Last modified by mathcam (2727)
Numerical id 9
Author mathcam (2727)
Entry type Theorem
Classification msc 11J81
Synonym Gelfond-Schneider Theorem
Related topic LindemannWeierstrassTheorem
Related topic Irrational