Modular Invariant of Rank 1 Drinfeld Modules and Class Field Generation

TL;DR

This paper introduces the modular invariant for rank 1 Drinfeld modules and uses it to establish an analog of the Weber-Fueter theorem, supported by a version of Shimura's Main Theorem for function fields.

Contribution

It formulates and proves an exact analog of the Weber-Fueter theorem for global function fields using the modular invariant of rank 1 Drinfeld modules.

Findings

Established the modular invariant for rank 1 Drinfeld modules.

Proved an analog of the Weber-Fueter theorem for function fields.

Proved a version of Shimura's Main Theorem of Complex Multiplication for global function fields.

Abstract

The modular invariant of rank 1 Drinfeld modules is introduced and used to formulate and prove an exact analog of the Weber-Fueter theorem for global function fields. The main ingredient in the proof is a version of Shimura's Main Theorem of Complex Multiplication for global function fields, which is also proved here.