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Modular functions and modular forms - James Milne

Modular functions and Modular forms (Elliptic Modular Curves) MilneVersion 22, 2017 This 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. 138 22, 2017. Corrected; minor revisions. 133 send comments and corrections to me at the address on my picture shows a fundamental domain for , as drawn by the fundamental domaindrawer of H.

Modular functions. A modular function f.z/of level Nis a meromorphic function on H invariant under .N/ and “meromorphic at the cusps”. Because it is invariant under .N/ , it can be regarded as a

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