Gene S. Kopp

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math.NT2026

SIC-POVMs and orders of real quadratic fields

Gene S. Kopp, Jeffrey C. Lagarias

This paper concerns SIC-POVMs and their relationship to class field theory. SIC-POVMs are generalized quantum measurements (POVMs) described by $d^{2}$ equiangular complex lines thro…

math.NT2026

Unit-generated orders of real quadratic fields I. Class number bounds

Gene S. Kopp, Jeffrey C. Lagarias

Unit-generated orders of a quadratic field are orders of the form $O = Z [ε]$ , where $ε$ is a unit in the quadratic field. If the order $\math…

math.NT2025

The Shintani--Faddeev modular cocycle: Stark units from $q$ -Pochhammer ratios

Gene S. Kopp

We give a new interpretation of Stark units associated to real quadratic fields as real multiplication values of a modular cocycle. The cocycle of interest is a meromorphic factor…

math.NT2025

A Constructive Approach to Zauner's Conjecture via the Stark Conjectures

Marcus Appleby, Steven T Flammia, Gene S Kopp

We propose a construction of $d^{2}$ complex equiangular lines in $C^{d}$ , also known as SICPOVMs, conjectured by Zauner to exist for all d. The construction gives a putativel…

math.NT2024

On $2$ -superirreducible polynomials over finite fields

Jonathan W. Bober, Lara Du, Dan Fretwell +2

We investigate $k$ -superirreducible polynomials, by which we mean irreducible polynomials that remain irreducible under any polynomial substitution of positive degree at most $k$ .…

SIC-POVMs and orders of real quadratic fields

Unit-generated orders of real quadratic fields I. Class number bounds

The Shintani--Faddeev modular cocycle: Stark units from q-Pochhammer ratios

A Constructive Approach to Zauner's Conjecture via the Stark Conjectures

On 2-superirreducible polynomials over finite fields

The Shintani--Faddeev modular cocycle: Stark units from $q$ -Pochhammer ratios

On $2$ -superirreducible polynomials over finite fields