Ring class invariants over imaginary quadratic fields

TL;DR

This paper demonstrates that specific singular values of quotients of the Δ-function generate ring class fields over imaginary quadratic fields, using Schertz's argument and Siegel-Ramachandra invariants.

Contribution

It introduces a novel approach to generating ring class fields via singular values of Δ-function quotients, extending previous methods.

Findings

Singular values of Δ-function quotients generate ring class fields.

Application of Schertz's argument with Siegel-Ramachandra invariants.

New insights into class field theory over imaginary quadratic fields.

Abstract

We show by adopting Schertz's argument with the Siegel-Ramachandra invariant that singular values of certain quotients of the $\Delta$-function generate ring class fields over imaginary quadratic fields.