Monogenity of pure quintic fields: the power of sieving
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866917478864519168 |
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| author | Gaál, István |
| author_facet | Gaál, István |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_03392 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Monogenity of pure quintic fields: the power of sieving Gaál, István Number Theory 11Y50, 11R04, 11D25 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. |
| title | Monogenity of pure quintic fields: the power of sieving |
| topic | Number Theory 11Y50, 11R04, 11D25 |
| url | https://arxiv.org/abs/2605.03392 |