Transcendence of e and π

@inproceedings{Jones1991TranscendenceOE,
  title={Transcendence of e and $\pi$},
  author={Arthur R. Jones and Kenneth R. Pearson and Sidney A. Morris},
  year={1991}
}
The main purpose of this chapter is to prove that the number π is transcendental, thereby completing the proof of the impossibility of squaring the circle (Problem III of the Introduction). We first give the proof that e is a transcendental number, which is somewhat easier. This is of considerable interest in its own right, and its proof introduces many of the ideas which will be used in the proof for π. With the aid of some more algebra — the theory of symmetric polynomials — we can then… 
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References

SHOWING 1-10 OF 17 REFERENCES
Transcendental Number Theory
First published in 1975, this classic book gives a systematic account of transcendental number theory, that is those numbers which cannot be expressed as the roots of algebraic equations having
An Introduction to the Theory of Numbers
This is the fifth edition of a work (first published in 1938) which has become the standard introduction to the subject. The book has grown out of lectures delivered by the authors at Oxford,
An alternative proof of the Lindemann-Weierstrass theorem
In December 1987 J. P. Bezivin and Ph. Robba found a new proof of the Lindemann-Weierstrass theorem as a by-product of their criterion of rationality for solutions of differential equations. Let us
A Course of Pure Mathematics
1. Real variables 2. Functions of real variables 3. Complex numbers 4. Limits of functions of a positive integral variable 5. Limits of functions of a continuous variable: continuous and
Elementary Mathematics from an Advanced Standpoint
THIS book continues the translation of Klein's “Elementar Mathematik” which Messrs. Hedrick and Noble began with their translation of the volume on arithmetic, algebra, and analysis. The volume under
Field Theory and its Classical Problems
1. Three Greek problems 2. Field extensions 3. Solution by radicals 4. Polynomials with symmetry groups.
Ueber die Transcendenz der Zahlen e und π
Man nehme an, die Zahl e genuge der Gleichung n ten Grades $$\alpha + {\alpha _1}e + {\alpha _2}{e^2} + \cdots + {\alpha _n}{e^n} = 0 $$ deren Coefficienten α, α 1, ..., α n ganze rationale
Ueber die Zahl π.*)
Bei der Vergeblichkeit der so ausserordentlich zahlreichen Versuche**), die Quadratur des Kreises mit Cirkel und Lineal auszufuhren, halt man allgemein die Losung der bezeichneten Aufgabe fur
Squaring the circle
Dissension in the British government about economic policy has wider implications.
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