2 citations · 3 across the 5 of their papers we have counts for
9 papers
Quadratic number fields with unramified -extensions
Joachim König
Continuing the line of thought of an earlier work, we provide the first infinite family of quadratic number fields with everywhere unramified Galois extensions of Galois group $SL_…
On parametric and generic polynomials with one parameter
Pierre Dèbes, Joachim König, François Legrand +1
Given fields , our results concern one parameter -parametric polynomials over , and their relation to generic polynomials. The former are polynomials $P(T,Y) \…
Covering groups of as regular Galois groups over
Joachim König
We close a gap in the literature by showing that the full covering groups of the Mathieu group and of its automorphism group occur as the Galois group of $\m…
Unramified extensions over low degree number fields
Joachim König, Danny Neftin, Jack Sonn
For various nonsolvable groups , we prove the existence of extensions of the rationals with Galois group and inertia groups of order dividing , where $ge…
On number fields with -free discriminants
Joachim König
Given a finite transitive permutation group , we investigate number fields of Galois group whose discriminant is only divisible by small prime powers. This ge…
Almost-Regular Dessins on a Sphere and Torus
Joachim König, Arielle Leitner, Danny Neftin
The Hurwitz problem asks which ramification data are realizable, that is appear as the ramification type of a covering. We use dessins d'enfant to show that families of genus 1 reg…