Analytic proof of the Lindemann - Weierstrass Theorem

[GoutamTmv]

Hey guys,

I would like to know whether there exists a proof for the Lindemann-Weierstrass Theorem that uses only the tools and techniques of elementary analysis.

If such a proof does not exist, I would like to know what would be the mathematical knowledge required to understand the proof.

 

[DonAntonio]

Hey guys,

I would like to know whether there exists a proof for the Lindemann-Weierstrass Theorem that uses only the tools and techniques of elementary analysis.

If such a proof does not exist, I would like to know what would be the mathematical knowledge required to understand the proof.

In this case I think that's nearly impossible: the very wording of the L-W theorem includes the notion of transcendence and fields extensions.

DonAntonio

 

[GoutamTmv]

Well then, what would be the minimum knowledge required to understand the proof?

Thanks in advance

 

[mathwonk]

I would suggest warming up to the proof by learning the proof in spivak's calculus that pi is irrational.

then consult the little carus mathematical monograph: irrational numbers, by ivan niven, chapter IX. in this book complete statements of all needed prerequisites are either proved, or given with references to places where they are proved, such as the carus monograph on algebraic numbers by harry pollard.