English

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

Number Theory 2018-08-17 v1 Group Theory

Abstract

If RR is the ring of integers of a number field, then there exists a polynomial parametrization of the set SL2(R)\text{SL}_2(R), i.e., an element ASL2(Z[x1,,xn])A \in \text{SL}_2(\mathbb{Z}[x_1,\ldots,x_n]) such that every element of SL2(R)\text{SL}_2(R) is obtained by specializing AA via some homomorphism Z[x1,,xn]R\mathbb{Z}[x_1,\ldots,x_n]\to R.

Keywords

Cite

@article{arxiv.1808.05349,
  title  = {Polynomial Parametrization for $\text{SL}_2$ over Quadratic Number Rings},
  author = {Michael Larsen and Dong Quan Ngoc Nguyen},
  journal= {arXiv preprint arXiv:1808.05349},
  year   = {2018}
}
R2 v1 2026-06-23T03:35:24.648Z