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Complex Multiplication by Reinhard Schertz

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6

Generation of ring class fields and ray class fields

The first two sections of this chapter are devoted to the classical constructions of ring class fields and ray class fields by singular values of j and the image function. This is the analogue of the construction of cyclotomic fields by roots of unity. However, the algebraic equation satisfied by the singular values of j and the image function are far from being as simple as the equations for roots of unity. Therefore, in the next sections we consider elliptic and modular functions other than j and ...

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