Titlebook: Elliptic Functions; Serge Lang Textbook 1987Latest edition Springer-Verlag New York Inc. 1987 Modular form.complex analysis.elliptic funct

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Automorphisms of the Modular Function FieldIf ., . are positive integers, and .|., then we have a canonical homomorphism .and we can take the projective limit.

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Complex MultiplicationWe first consider values of the .-function at quadratic imaginary numbers. We shall see that these values generate abelian extensions of quadratic fields.

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The ι-adic and p-adic Representations of DeuringIt was first proved by Hasse that even in characteristic . > 0, if . is an integer prime to ., then the points of order . on an elliptic curve . form a cyclic group of type ./. x ./..

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