fundamental theorems in complex analysis
The following is a list of fundamental theorems in the subject of complex analysis (single complex variable). If a theorem does not yet appear in the encyclopedia, please consider adding it — Planet Math is a work in progress and some basic results have not yet been entered. Likewise, if some basic theorem has been overlooked in this list, please add it.
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Cauchy’s integral^{} theorem
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Morera’s theorem

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Cauchy’s integral formula

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Cauchy’s residue theorem^{}

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Cauchy’s argument principle

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Rouché’s theorem
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Riemann’s removable singularity^{} theorem
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implicit function theorem^{} for complex analytic functions (I gave proofs of this and the next theorem in a posting to a forum and must convert them to an encyclopaedia entry.)

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inverse function theorem for complex analytic functions
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Liouville’s theorem

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characterization of rational functions

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Weierstrass’ factorization theorem

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Weierstrass’ criterion of uniform convergence^{}

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MittagLeffler’s theorem

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MÃÂ¶bius circle transformation theorem
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Gauss’ mean value theorem

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Schwarz’ reflection principle

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Harnack’s principle

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Bloch theorem

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Picard’s theorem (http://planetmath.org/PicardsTheorem)
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Runge’s theorem

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Mergelyan’s theorem

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Montel’s theorem

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Marty’s theorem

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Hurwitz’s theorem

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Bieberbach’s conjecture
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Factorization theorem for ${H}^{\mathrm{\infty}}$ functions^{} (http://planetmath.org/FactorizationTheoremForHinftyFunctions)
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Title  fundamental theorems in complex analysis 

Canonical name  FundamentalTheoremsInComplexAnalysis 
Date of creation  20130322 14:57:33 
Last modified on  20130322 14:57:33 
Owner  rspuzio (6075) 
Last modified by  rspuzio (6075) 
Numerical id  26 
Author  rspuzio (6075) 
Entry type  Topic 
Classification  msc 3000 
Related topic  TopicEntryOnComplexAnalysis 