Monotone polygon

Mathematics education

Pure mathematics

Discrete mathematics

Equiangular polygon

Algebraic number field

Field (mathematics)

Computer science

Mathematics

Unit (ring theory)

Quadratic equation

Discriminant

Mathematical analysis

Artificial intelligence

Geometry

Combinatorics

Logarithm

Conjecture

Finite field

Class (philosophy)

Acta Arithmetica

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.

Generating ray class fields of real quadratic fields via complex equiangular lines