Generating ray class fields of real quadratic fields via complex equiangular lines
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 summarise this in a conjecture. There are indications [19,20] 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.