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Lhoussain El Fadil

Publications and source records attributed to Lhoussain El Fadil.

21 records · Page 2Linked to original sources

arXiv2018

On the Extensions of a Discrete Valuation in a Number Field

Let $K$ be a number field defined by a monic irreducible polynomial $F(X) \in \mathbb{Z}[X]$, $p$ a fixed rational prime, and $ν_p$ the discrete valuation associated to $p$. Assume that $\overline{F}(X)$ factors modulo $p$ into the product of powers of $r$ distinct monic irreducible polynomials. We present in this paper a condition, weaker than the known ones, which guarantees the existence of exactly $r$ valuations of $K$ extending $ν_p$. We further specify the ramification indices and residue degrees of these extended valuations in such a way that generalizes the known estimates. Some useful remarks and computational examples are also given to highlight some improvements due to our result.

math.NT↗

arXiv2010

Explicit Factorization of Prime Integers in Quartic Number Fields defined by $X^4+aX+b$

For every prime integer $p$, an explicit factorization of the principal ideal $p\z_K$ into prime ideals of $\z_K$ is given, where $K$ is a quartic number field defined by an irreducible polynomial $X^4+aX+b\in\z[X]$.

math.NT↗

arXiv2009

Computation of an Integral Basis of Quartic Number Fields

In this paper, based on techniques of Newton polygons, a result which allows the computation of a p integral basis of every quartic number field is given. For each prime integer p, this result allows to compute a p-integral basis of a quartic number field K defined by an irreducible polynomial $P(X) = X4 + aX + b \in\z[X]$ in methodical and complete generality.

math.NT↗