Calculating power integral bases by solving relative Thue equations
Number Theory
2018-10-04 v1
Abstract
In our recent paper we gave an efficient algorithm to calculate "small" solutions of relative Thue equations (where "small" means an upper bound of type for the sizes of solutions). Here we apply this algorithm to calculating power integral bases in sextic fields with an imaginary quadratic subfield and to calculating relative power integral bases in pure quartic extensions of imaginary quadratic fields. In both cases the crucial point of the calculation is the resolution of a relative Thue equation. We produce numerical data that were not known before.
Cite
@article{arxiv.1810.01820,
title = {Calculating power integral bases by solving relative Thue equations},
author = {István Gaál and László Remete and Tí mea Szabó},
journal= {arXiv preprint arXiv:1810.01820},
year = {2018}
}