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

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.

This is a substantial revision of the previous version. The ray class fields have been modified, and are now defined using quadratic orders, so as to have number field counterparts. There is a new section discussing the adaptation of the ideas in this paper to the number field setting, which conjecturally would give ray class field generation there as well