A note on universal Hilbert sets.
Abundance of Hilbertian domains.
Acknowledgement of priority
Almost hilbertian fields
This paper is devoted to some variants of the Hilbert specialization property. For example, the RG-hilbertian property (for a field K), which arose in connection with the Inverse Galois Problem, requires that the specialization property holds solely for extensions of K(T) that are Galois and regular over K. We show that fields inductively obtained from a real hilbertian field by adjoining real pth roots (p odd prime) are RG-hilbertian; some of these fields are not hilbertian. There are other variants...
An irreducibility criterion for polynomials in several variables
Compositum of Galois extensions of hilbertian fields
Der Hilbertsche Irreduzibilitätssatz.
Der Hilbertsche Irreduzibilitätssatz und Primzahlfragen.
Einfacher Beweis des Hilbertschen Irreduzibilitätssatzes
Equations in the Hadamard ring of rational functions
Let be a number field. It is well known that the set of recurrencesequences with entries in is closed under component-wise operations, and so it can be equipped with a ring structure. We try to understand the structure of this ring, in particular to understand which algebraic equations have a solution in the ring. For the case of cyclic equations a conjecture due to Pisot states the following: assume is a recurrence sequence and suppose that all the have a root in the field ; then (after...
Fields containing values of algebraic functions
Fields containing values of algebraic functions II (On a conjecture of Schinzel)
Finiteness results for Hilbert's irreducibility theorem
Let be a number field, its ring of integers, and be an irreducible polynomial. Hilbert’s irreducibility theorem gives infinitely many integral specializations such that is still irreducible. In this paper we study the set of those with reducible. We show that is a finite set under rather weak assumptions. In particular, previous results obtained by diophantine approximation techniques, appear as special cases of some of our results. Our method is different. We use elementary group...
Frattini-Einbettungsprobleme über Hilbertkörpern.
Galois Covers and the Hilbert-Grunwald Property
Our main result combines three topics: it contains a Grunwald-Wang type conclusion, a version of Hilbert’s irreducibility theorem and a -adic form à la Harbater, but with good reduction, of the Regular Inverse Galois Problem. As a consequence we obtain a statement that questions the RIGP over . The general strategy is to study and exploit the good reduction of certain twisted models of the covers and of the associated moduli spaces.
Galois covers with prescribed fibers : the Beckmann-Black problem
Hilbert sets and zeta functions over finite fields.
Hilbert Subsets and s-Integral Points.
Le théorème d'irréductibilité de Hilbert
On a problem of Dvornicich and Zannier