Contents

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16.1. Continuation along Curves

16.2. The Complete Analytic Function

16.3. Unrestricted Continuation — the Monodromy Theorem

16.4. Another Point of View

Chapter 17. Orientation

Chapter 18. The Modular Function

Chapter 19. Preliminaries for the Picard Theorems

19.0. Holomorphic Covering Maps

19.1. Examples of Holomorphic Covering Maps

19.2. Two More Automorphism Groups

19.3. Normalizers of Covering Groups

19.4. Covering Groups and Conformal Equivalence

Chapter 20. The Picard Theorems

Part 2. Further Results

Chapter 21. Abel's Theorem

Chapter 22. More on Brownian Motion

Chapter 23. More on the Maximum Modulus Theorem

23.0. Theorems of Hadamard and Phragmen-Lindelof

23.1. An Application: The Hausdorff-Young Inequality

Chapter 24. The Gamma Function

Chapter 25. Universal Covering Spaces

Chapter 26. Cauchy's Theorem for Nonholomorphic Functions

Chapter 27. Harmonic Conjugates

Part 3. Appendices

Appendix 1. Complex Numbers

Appendix 2. Complex Numbers, Continued

Appendix 3. Sin, Cos and

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