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

Tremor

Differenzial- und Integralrechung,We 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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Differenzierbarkeit und AbleitungenLet . be the modular function field, studied in Chapter 6. We saw that . can be identified with the field of .-coordinates (or .-coordinates, . = Weber function) of division points of an elliptic curve . defined over .(.), having invariant .. Let . be an imaginary quadratic field, and let . ∈ . ⋂ ℌ

Explicate

Diskrete Fourier-TransformationIn this section we give an example for the Shimura theorem concerning the quotient of automorphic functions.

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懦夫

EVADE

CANON

Elliptic FunctionsBy a . in the complex plane . we shall mean a subgroup which is free of dimension 2 over ., and which generates . over the reals. If ω., ω. is a basis of a lattice . over ., then we also write . = [ω., ω.].

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巨硕

The Modular FunctionBy . we mean the group of 2 x 2 matrices with determinant 1. We write . (.) for those elements of . having coefficients in a ring .. In practice, the ring . will be ., ., .. We call . (.) the ..

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