FORMULAS OF GALOIS ACTIONS OF SOME CLASS INVARIANTS OVER QUADRATIC NUMBER FIELDS WITH DISCRIMINANT D ≡ 1 (mod 12)

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 some class invariants from the generalized Weber functions g0, g1, g2 and g3 over quadratic number fields with discriminant D ≡ 1 (mod 12).

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