Quantum Drinfeld Modules and Ray Class Fields of Real Quadratic Global Function Fields

TL;DR

This paper advances the understanding of explicit class field theory for real quadratic function fields in positive characteristic by providing a solution to Hilbert's 12th problem, and explores conjectural analogs for number fields using quasicrystals.

Contribution

It presents a solution to Hilbert's 12th problem for real quadratic function fields and proposes a conjectural framework for number fields using quasicrystal analogs.

Findings

Constructs explicit generators for ray class fields of real quadratic function fields.

Proves an analog of the Weber-Fueter theorem in the function field setting.

Suggests a new approach to class field theory for number fields via quasicrystals.

Abstract

This is the second in a series of two papers presenting a solution to Hilbert's 12th problem for real quadratic function fields in positive characteristic, in the sense of proving an analog of the Theorem of Weber-Fueter. We also offer a conjectural treatment of the number field case using quasicrystal counterparts of the constructions used in function fields.