2 citations · 3 across the 10 of their papers we have counts for
14 papers · 1 filter
The Davenport-Lewis-Schinzel problem on the reducibility of
Angelot Behajaina, Joachim König, Danny Neftin
We solve the problem of Davenport--Lewis--Schinzel (DLS), originating in the 1950s, regarding the reducibility of . This yields an almost-complete solut…
A note on monogenic even polynomials
Joachim König
We extend several predecessor works on even sextic monogenic polynomials. In particular, we prove a conjecture of Lenny Jones, thereby classifying even sextic monogenic polynomials…
Unramified extensions of quadratic number fields with Galois group
Joachim König
We realize infinitely many covering groups (where is the alternating group) as the Galois group of everywhere unramified Galois extensions over infinitely many quadra…
Integrally Hilbertian rings and the polynomial Schinzel hypothesis
Angelot Behajaina, Pierre Dèbes, Joachim König
The classical Hilbert specialization property is a field-theoretic tool ensuring that polynomial irreducibility over a field is preserved under specialization of some of the variab…
Critical Point Criteria and Dynamically Monogenic Polynomials
Joachim König, Hanson Smith, Zack Wolske
Let be a number field with ring of integers , and let be a monic, irreducible polynomial. We establish necessary and sufficient conditi…
Linear constellations in primes with arithmetic restrictions
Christopher Frei, Joachim König, Magdaléna Tinková
We prove analogues of the theorem of Green and Tao on linear constellations in primes, in which the primes under consideration are restricted by certain arithmetic conditions. Our…