Generating ray class fields of real quadratic fields via complex equiangular lines
Volume 192 / 2020
Abstract
For certain real quadratic fields $K$ with sufficiently small discriminant we produce explicit unit generators for specific ray class fields of $K$ using a numerical method that arose in the study of complete sets of equiangular lines in $\mathbb{C}^d $ (known in quantum information as symmetric informationally complete measurements, or SICs). The construction in low dimensions suggests a general recipe for producing unit generators in infinite towers of ray class fields above arbitrary real quadratic $K$, and we summarize this in a conjecture. There are indications in G. S. Kopp’s work that the logarithms of these canonical units are related to the values of L-functions associated to the extensions, following the programme laid out in the Stark Conjectures.
