GALOIS ACTIONS OF A CLASS INVARIANT OVER QUADRATIC NUMBER FIELDS WITH DISCRIMINANT D ≡ −3 (mod 36)

Abstract

A class invariant is the value of a modular function that generates a ring class field of an imaginary quadratic number field such as the singular moduli of level 1. In this paper, using Shimura Reciprocity Law, we compute the Galois actions of a class invariant from a generalized Weber function g2 over quadratic number fields with discriminant D ≡ −3 (mod 36).

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