Monogenity of pure quintic fields: the power of sieving
Number Theory
2026-05-12 v2
Abstract
We provide a simple algorithm for calculating all generators of power integral bases in pure quintic fields. This procedure involves the usual standard elements like Baker's method, LLL-reduction. The main purpose of the paper is to introduce a new idea to considerably diminish the number of small exponents to be considered after the reduction step. This new idea allows to test all remaining small exponents within a few minutes, using an appropriate sieve method, which turns out to be surprisingly fast. This idea will be applicable in many similar cases.
Cite
@article{arxiv.2605.03392,
title = {Monogenity of pure quintic fields: the power of sieving},
author = {István Gaál},
journal= {arXiv preprint arXiv:2605.03392},
year = {2026}
}