Siegel families with application to class fields

TL;DR

This paper explores families of Siegel modular functions and uses Shimura's reciprocity law to construct algebraic numbers in ray class fields of CM-fields from special function values.

Contribution

It introduces specific Siegel families and demonstrates their application in explicitly constructing class fields of CM-fields.

Findings

Construction of algebraic numbers in ray class fields

Application of Shimura's reciprocity law to Siegel functions

Explicit formulas for class field generation

Abstract

We investigate certain families of meromorphic Siegel modular functions on which Galois groups act in a natural way. By using Shimura's reciprocity law we construct some algebraic numbers in the ray class fields of CM-fields in terms of special values of functions in these Siegel families.