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Vincenzo Acciaro

Publications and source records attributed to Vincenzo Acciaro.

5 recordsLinked to original sources
arXiv2020

Some split symbol algebras of prime degree

Let $p$ be an odd prime, let $K=\mathbb{Q}(ε)$ where $ε$ is a primitive cubic root of unity, and let $L$ be the Kummer field $\mathbb{Q}\left(ε, \sqrt[3]α\right)$. In this paper we obtain a characterization of the splitting behavior of the symbol algebras $\left( \frac{α,p}{K,ε}\right)$ and $\left( \frac{α,p^{h_{p}}}{K,ε}\right)$, where $h_{p}$ is the order in the class group $Cl\left(L\right)$ of a prime ideal of $\mathcal{O}_L$ which divides $p\mathcal{O}_L.$

math.NT↗
arXiv2020

On quaternion algebras over some extensions of quadratic number fields

Let $p$ and $q$ be two positive primes. Let $\ell$ be an odd positive prime integer and $F$ a quadratic number field. Let $K$ be an extension of $F$ such that $K$ is a dihedral extension of $\Q$ of degree $\ell$ over $F$ or $K$ is an abelian $\ell$-extension unramified over $F$ assuming $\ell$ divides the class number of $F$. In this paper, we obtain a complete characterization of division quaternion algebras $H_{K}(p, q)$ over $K$.

math.NT↗
arXiv2019

On quaternion algebras that split over quadratic number fields

Let $d$ and $m$ be two distinct squarefree integers and $\mathcal{O}_K$ the ring of integers of the quadratic field $K=\mathbb{Q}(\sqrt{d})$. Denote by $ H_K(α, m)$ a quaternion algebra over $K$, where $α\in \mathcal{O}_K$. In this paper we give necessary and sufficient conditions for $ H_K(α, m)$ to split over $K$ for some values of $α$, and we obtain a complete characterization of division quaternion algebras $ H_K(α, m)$ over $K$ whenever $α$ and $m$ are two distinct positive prime integers. Examples are given involving prime Fibonacci numbers.

math.NT↗
arXiv2017

Computing normal integral bases of abelian number fields

Let L be an abelian number field of degree n with Galois group G. In this paper we study how to compute efficiently a normal integral basis for L, if there is at least one, assuming that the group G and an integral basis for L are known.

math.NT↗