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Weber's class invariants revisited

Reinhard Schertz (2002)

Journal de théorie des nombres de Bordeaux

Let K be a quadratic imaginary number field of discriminant d . For t let 𝔒 t denote the order of conductor t in K and j ( 𝔒 t ) its modular invariant which is known to generate the ring class field modulo t over K . The coefficients of the minimal equation of j ( 𝔒 t ) being quite large Weber considered in [We] the functions f , f 1 , f 2 , γ 2 , γ 3 defined below and thereby obtained simpler generators of the ring class fields. Later on the singular values of these functions played a crucial role in Heegner’s solution [He] of the class...

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