Solubility for families of norm equations coming from abelian number fields
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866910129929060352 |
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| author | Da Silva, Mathieu |
| author_facet | Da Silva, Mathieu |
| contents | For $F \in \mathbb{Z}[s,t]$ a binary quadratic form which is irreducible over $\mathbb{Q}$, and $L$ an abelian number field with class number $1$, we obtain the order of magnitude for the number of values $F(s,t)$ which are a norm from $L$. Our result relies on the fundamental lemma of sieve theory and on geometry of numbers. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_12697 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Solubility for families of norm equations coming from abelian number fields Da Silva, Mathieu Number Theory For $F \in \mathbb{Z}[s,t]$ a binary quadratic form which is irreducible over $\mathbb{Q}$, and $L$ an abelian number field with class number $1$, we obtain the order of magnitude for the number of values $F(s,t)$ which are a norm from $L$. Our result relies on the fundamental lemma of sieve theory and on geometry of numbers. |
| title | Solubility for families of norm equations coming from abelian number fields |
| topic | Number Theory |
| url | https://arxiv.org/abs/2604.12697 |