On some Fricke families and application to the Lang-Schertz conjecture

TL;DR

This paper explores specific Fricke families of functions and their special values to generate ray class fields of imaginary quadratic fields, providing insights into the Lang-Schertz conjecture.

Contribution

It introduces new methods using Fricke and Siegel functions to generate ray class fields, advancing understanding of the Lang-Schertz conjecture.

Findings

Generated ray class fields from special values of Fricke and Siegel functions

Established connections between Fricke families and class field theory

Provided evidence supporting the Lang-Schertz conjecture

Abstract

We first investigate two kinds of Fricke families consisting of Fricke functions and Siegel functions, respectively. And, in terms of their special values we generate ray class fields of imaginary quadratic fields, which is related to the Lang-Schertz conjecture.