Polynomial Parametrization for SL2 over Quadratic Number Rings

Abstract

If $R$ is the ring of integers of a number field, then there exists a polynomial parametrization of the set $\operatorname{SL}_2(R)$, that is, an element $A\in{\textrm{SL}}_2(\mathbb{Z}[x_1,\ldots ,x_n])$ such that every element of $\operatorname{SL}_2(R)$ is obtained by specializing $A$ via some homomorphism $\mathbb{Z}[x_1,\ldots ,x_n]\to R$.

Document Details

Document Type
Pub Defense Publication
Publication Date
Mar 13, 2019
Source ID
10.1093/imrn/rnz046

Entities

People

  • Dong Quan Ngoc Nguyen
  • Michael B. Larsen

Organizations

  • Defense Advanced Research Projects Agency
  • Indiana University
  • National Science Foundation
  • University of Notre Dame

Tags

Fields of Study

  • Mathematics

Readers

  • Analytical Mechanics
  • Graph Algorithms and Convex Optimization.