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arXiv · 2605.03392

Monogenity of pure quintic fields: the power of sieving

István Gaál
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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.

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István Gaál. 2026-05-05. Monogenity of pure quintic fields: the power of sieving. https://arxiv.org/abs/2605.03392

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