François Legrand

activity

20132022

most citedCloaking, Trapping and Superlensing of Lamb Waves with Negative Refraction

21 citations · 40 across the 8 of their papers we have counts for

collaborators

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13 papers · 1 filter

math.NT2021

On a variant of the Beckmann--Black problem

François Legrand

Given a field $k$ and a finite group $G$ , the Beckmann--Black problem asks whether every Galois field extension $F / k$ with group $G$ is the specialization at some $t_{0} \in k$ of so…

math.NT2020★ 4 cited

Galois groups over rational function fields over skew fields

Gil Alon, François Legrand, Elad Paran

Let $H$ be a skew field of finite dimension over its center $k$ . We solve the Inverse Galois Problem over the field of fractions $H (X)$ of the ring of polynomial functions over $H$ …

math.NT2019

Galois families of modular forms and application to weight one

Sara Arias-de-Reyna, François Legrand, Gabor Wiese

We introduce Galois families of modular forms. They are a new kind of family coming from Galois representations of the absolute Galois groups of rational function fields over the r…

math.NT2019★ 3 cited

Density results for specialization sets of Galois covers

Joachim König, François Legrand

We provide evidence for this conclusion: given a finite Galois cover $f : X \to P_{Q}^{1}$ of group $G$ , almost all (in a density sense) realizations of $G$ ov…

math.NT2018

Embedding problems for automorphism groups of field extensions

Arno Fehm, François Legrand, Elad Paran

A central conjecture in inverse Galois theory, proposed by Dèbes and Deschamps, asserts that every finite split embedding problem over an arbitrary field can be regularly solved. W…

math.NT2018

Rational pullbacks of Galois covers

Pierre Dèbes, Joachim König, François Legrand +1

The finite subgroups of $PGL_{2} (C)$ are shown to be the only finite groups $G$ with this property: for some integer $r_{0}$ (depending on $G$ ), all Galois covers $X\rig…

math.NT2016

Non-parametric sets of regular realizations over number fields

Joachim König, François Legrand

Given a number field $k$ , we show that, for many finite groups $G$ , all the Galois extensions of $k$ with Galois group $G$ cannot be obtained by specializing any given finitely man…

math.NT2016

Twists of superelliptic curves without rational points

François Legrand

Let $n \geq 2$ be an integer, $F$ a number field, $O_{F}$ the integral closure of $Z$ in $F$ and $N$ a positive multiple of $n$ . The paper deals with degree $N$ polynomials $…

math.NT2016

On parametric extensions over number fields

François Legrand

Given a number field $F$ , a finite group $G$ and an indeterminate $T$ , {\it{a $G$ -parametric extension over $F$ }} is a finite Galois extension $E / F (T)$ with Galois group $G$ and $E…

math.NT2015

On the number of ramified primes in specializations of function fields over $Q$

Lior Bary-Soroker, François Legrand

We study the number of ramified prime numbers in finite Galois extensions of $Q$ obtained by specializing a finite Galois extension of $Q (T)$ . Our main result is…

math.NT2014

Hilbert specialization results with local conditions

François Legrand

Given a field $k$ of characteristic zero and an indeterminate $T$ , the main topic of the paper is the construction of specializations of any given finite extension of $k (T)$ of deg…

math.NT2013

Parametric Galois Extensions

François Legrand

Given a field $k$ and a finite group $H$ , {\it{an $H$ -parametric extension over $k$ }} is a finite Galois extension of $k (T)$ of Galois group containing $H$ which is regular over $k…

math.NT2013

Specialization results and ramification conditions

François Legrand

Given a hilbertian field $k$ of characteristic zero and a finite Galois extension $E / k (T)$ with group $G$ such that $E / k$ is regular, we produce some specializations of $E / k (T)$ at…

On a variant of the Beckmann--Black problem

Galois groups over rational function fields over skew fields

Galois families of modular forms and application to weight one

Density results for specialization sets of Galois covers

Embedding problems for automorphism groups of field extensions

Rational pullbacks of Galois covers

Non-parametric sets of regular realizations over number fields

Twists of superelliptic curves without rational points

On parametric extensions over number fields

On the number of ramified primes in specializations of function fields over Q

Hilbert specialization results with local conditions

Parametric Galois Extensions

Specialization results and ramification conditions

On the number of ramified primes in specializations of function fields over $Q$