Solubility for families of norm equations coming from abelian number fields

Mathieu Da Silva

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arXiv · 2604.12697

Solubility for families of norm equations coming from abelian number fields

Mathieu Da Silva

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Abstract

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.

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Mathieu Da Silva. 2026-04-14. Solubility for families of norm equations coming from abelian number fields. https://arxiv.org/abs/2604.12697

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