Lindemann-Weierstrass Theorem

If algebraic integers alpha_1, ..., alpha_n are linearly independent over Q, then e^(alpha_1), ..., e^(alpha_n) are algebraically independent over Q. The Lindemann-Weierstrass theorem is implied by Schanuel's conjecture (Chow 1999).

See also

Algebraically Independent, Hermite-Lindemann Theorem, Schanuel's Conjecture

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Baker, A. Theorem 2.1 in Transcendental Number Theory. Cambridge, England: Cambridge University Press, 1990.Chow, T. Y. "What is a Closed-Form Number?" Amer. Math. Monthly 106, 440-448, 1999.

Referenced on Wolfram|Alpha

Lindemann-Weierstrass Theorem

Cite this as:

Weisstein, Eric W. "Lindemann-Weierstrass Theorem." From MathWorld--A Wolfram Web Resource.

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