Counting ideals in abelian number fields
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866917170798133248 |
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| author | Languasco, Alessandro Lunia, Rashi Moree, Pieter |
| author_facet | Languasco, Alessandro Lunia, Rashi Moree, Pieter |
| contents | Already Dedekind and Weber considered the problem of counting integral ideals of norm at most $x$ in a given number field $K$. Here we improve on the existing results in case $K/\mathbb Q$ is abelian and has degree at least four. For these fields, we obtain as a consequence an improvement of the available results on counting pairs of coprime ideals each having norm at most $x$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_09469 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Counting ideals in abelian number fields Languasco, Alessandro Lunia, Rashi Moree, Pieter Number Theory 11R42, 11M41 Already Dedekind and Weber considered the problem of counting integral ideals of norm at most $x$ in a given number field $K$. Here we improve on the existing results in case $K/\mathbb Q$ is abelian and has degree at least four. For these fields, we obtain as a consequence an improvement of the available results on counting pairs of coprime ideals each having norm at most $x$. |
| title | Counting ideals in abelian number fields |
| topic | Number Theory 11R42, 11M41 |
| url | https://arxiv.org/abs/2504.09469 |