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Complex Multiplication by Reinhard Schertz

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7

Integral basis in ray class fields

We start by some motivating remarks on cyclotomic fields. Let f > 1 be a natural number and ζ a primitive f-th root of unity. Then

is the ray class field modulo over , and ζ is known to generate a power basis over for the ring of integers f in kf :

Therefore, the ray class field modulo over is generated by a ...

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