Polynomial Parametrization for ${\text{SL}}_2$ over Quadratic Number Rings

Michael Larsen, Dong Quan Ngoc Nguyen

If $R$ is the ring of integers of a number field, then there exists a polynomial parametrization of the set ${\text{SL}}_2(R)$, i.e., an element $A \in \text{SL}_2(\mathbb{Z}[x_1,\ld…