Lindemann–Weierstrass theorem
Theorem in transcendental number theory
Lindemann–Weierstrass theorem
In transcendental number theory, the Lindemann–Weierstrass theorem is a result that is very useful in establishing the transcendence of numbers. It states the following: In other words, the extension field Q ( e α 1 , … , e α n ) {\displaystyle \mathbb {Q} (e^{\alpha _{1}},\dots ,e^{\alpha _{n}})} has transcendence degree n over Q {\displaystyle \mathbb {Q} } . An equivalent formulation from Baker 1990, Chapter 1, Theorem 1.4, is the following: This equivalence transforms a linear relation over the algebraic numbers into an algebraic relation over...
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