Transcendental Numbers

Table of Contents

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   Book Overview
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   Chapter 1 Liouville’s Theorem
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   Chapter 2 Hermite’s Theorem
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   Chapter 3 Lindemann’s Theorem
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   Chapter 4 The Lindemann–Weierstrass Theorem
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   Chapter 5 The Maximum Modulus Principle and Its Applications
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   Chapter 6 Siegel’s Lemma
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   Chapter 7 The Six Exponentials Theorem
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   Chapter 8 Estimates for Derivatives
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    Chapter 9 The Schneider–Lang Theorem
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    Chapter 10 Elliptic Functions
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    Chapter 11 Transcendental Values of Elliptic Functions
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    Chapter 12 Periods and Quasiperiods
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    Chapter 13 Transcendental Values of Some Elliptic Integrals
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    Chapter 14 The Modular Invariant
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    Chapter 15 Transcendental Values of the j -Function
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    Chapter 16 More Elliptic Integrals
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    Chapter 17 Transcendental Values of Eisenstein Series
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    Chapter 18 Elliptic Integrals and Hypergeometric Series
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    Chapter 19 Baker’s Theorem
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    Chapter 20 Some Applications of Baker’s Theorem
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    Chapter 21 Schanuel’s Conjecture
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    Chapter 22 Transcendental Values of Some Dirichlet Series
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    Chapter 23 The Baker–Birch–Wirsing Theorem
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    Chapter 24 Transcendence of Some Infinite Series
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    Chapter 25 Linear Independence of Values of Dirichlet L -Functions
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    Chapter 26 Transcendence of Values of Class Group L -Functions
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    Chapter 27 Transcendence of Values of Modular Forms
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    Chapter 28 Periods, Multiple Zeta Functions and ζ (3)