Joachim Konig

collaborators

3 papers

math.NT2026

Integrally Hilbertian rings and the polynomial Schinzel hypothesis

Angelot Behajaina, Pierre DÃ¨bes, Joachim KÃ¶nig

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…

math.NT2026

The Davenport-Lewis-Schinzel problem on the reducibility of $f (X) - g (Y)$

Angelot Behajaina, Joachim KÃ¶nig, Danny Neftin

We solve the problem of Davenport--Lewis--Schinzel (DLS), originating in the 1950s, regarding the reducibility of $f (X) - g (Y) \in C [X, Y]$ . This yields an almost-complete solut…

math.NT2024

Polynomial compositions with large monodromy groups and applications to arithmetic dynamics

Joachim KÃ¶nig, Danny Neftin, Shai Rosenberg

For a composition $f = f_{1} \circ \dots \circ f_{r}$ of polynomials $f_{i} \in Q [x]$ of degrees $d_{i} \geq 5$ with alternating or symmetric monodromy group, we show that the monodromy…

Integrally Hilbertian rings and the polynomial Schinzel hypothesis

The Davenport-Lewis-Schinzel problem on the reducibility of f(X)−g(Y)

Polynomial compositions with large monodromy groups and applications to arithmetic dynamics

The Davenport-Lewis-Schinzel problem on the reducibility of $f (X) - g (Y)$