Quantum Drinfeld Modules and Ray Class Fields of Real Quadratic Global Function Fields
Number Theory
2024-07-04 v4
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.
Keywords
Cite
@article{arxiv.1709.05337,
title = {Quantum Drinfeld Modules and Ray Class Fields of Real Quadratic Global Function Fields},
author = {L. Demangos and T. M. Gendron},
journal= {arXiv preprint arXiv:1709.05337},
year = {2024}
}
Comments
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