Richard Scarlini

Principal-unit Di\c{t}\u{a}-type Butson matrices: character-table transitions, fractional-linear automorphisms, Weyl thresholds, and polarized Heisenberg windows

For an odd prime $p$ and integers $r,q\ge 1$, we study the Butson-type complex Hadamard matrices $H_{p;r,q}(a,b)=\chi(1+p^r ab)$ on $\mathbb{Z}/p^q\mathbb{Z}$, where $\chi$ is a faithful character of the principal-unit quotient. The defining phase is the normalized $p$-adic logarithm, linear modulo $p^q$ exactly when $...