Modular functions and modular forms - James Milne

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Modular functions and Modular forms (Elliptic Modular Curves) MilneVersion 22, 2017This is an introduction to the arithmetic theory of Modular functions and Modular forms ,with a greater emphasis on the geometry than most information:@misc{milneMF,author={ Milne , James S.},title={ Modular functions and Modular forms ( )},year={2017},note={Available at },pages={134}} 22, 1997; first version on the web; 128 23, 2009; new style; minor fixes and improvements; added list of symbols;129 26, 2010. Corrected; many minor revisions.

case of the theorem says that every simply connected open subset of C different from C is isomorphic to D. This is proved in Cartan 1963, VI, ’3. The general statement is the famous Uniformization Theorem, which was proved independently by Koebe and Poincare in 1907.´ See mo10516 for a discussion of the various proofs. 2 5

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