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Currently displaying 1 – 3 of 3

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Comment on the remark by G.A. Kurina on the paper (Müller, 1998)

Peter Müller — 2002

International Journal of Applied Mathematics and Computer Science

Finiteness results for Hilbert's irreducibility theorem

Peter Müller — 2002

Annales de l’institut Fourier

Let $k$ be a number field, $𝒪_{k}$ its ring of integers, and $f (t, X) \in k (t) [X]$ be an irreducible polynomial. Hilbert’s irreducibility theorem gives infinitely many integral specializations $t \mapsto \bar{t} \in 𝒪_{k}$ such that $f (\bar{t}, X)$ is still irreducible. In this paper we study the set ${Red}_{f} (𝒪_{k})$ of those $\bar{t} \in 𝒪_{k}$ with $f (\bar{t}, X)$ reducible. We show that ${Red}_{f} (𝒪_{k})$ 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...

Sharply 2-transitive sets of permutations and groups of affine projectivities.

Grundhöfer, Theo; Müller, Peter — 2009

Beiträge zur Algebra und Geometrie

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