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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.
We give an explicit construct of a harmonic weak Maass form $F_{Theta}$ that is a lift of $Theta^3$, where $Theta$ is the classical Jacobi theta function. Just as the Fourier coefficients of $Theta^3$ are related to class numbers of imaginary quadrat
In this paper, we explicitly construct harmonic Maass forms that map to the weight one theta series associated by Hecke to odd ray class group characters of real quadratic fields. From this construction, we give precise arithmetic information contain
Let $K$ be a quartic CM field, that is, a totally imaginary quadratic extension of a real quadratic number field. In a 1962 article titled On the classfields obtained by complex multiplication of abelian varieties, Shimura considered a particular fam
We investigate equiangular lines in finite orthogonal geometries, focusing specifically on equiangular tight frames (ETFs). In parallel with the known correspondence between real ETFs and strongly regular graphs (SRGs) that satisfy certain parameter
We study a form of refined class number formula (resp. type number formula) for maximal orders in totally definite quaternion algebras over real quadratic fields, by taking into consideration the automorphism groups of right ideal classes (resp. unit