Greatest common divisors of values of integer polynomials and an application to maximal tori

Frank Lübeck

Greatest common divisors of values of integer polynomials and an application to maximal tori

Group Theory 2023-08-23 v1 Number Theory

Authors: Frank Lübeck

Abstract

We describe how to compute for two polynomials $f(X), g(X) \in \mathbb{Z}[X]$ with integer coefficients the greatest common divisors of $f(z)$ and $g(z)$ for all integers $z \in \mathbb{Z}$ . As an application we determine the structures (elementary divisors) of all maximal tori in exceptional groups of Lie type.

Keywords

integer polynomials greatest common divisor maximal tori exceptional groups of lie type elementary divisors computation

Cite

@article{arxiv.2308.10971,
  title  = {Greatest common divisors of values of integer polynomials and an application to maximal tori},
  author = {Frank Lübeck},
  journal= {arXiv preprint arXiv:2308.10971},
  year   = {2023}
}

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