On Hilbert's irreducibility theorem

Abel Castillo, Rainer Dietmann

Research output: Contribution to journalArticlepeer-review

52 Downloads (Pure)


We obtain new quantitative forms of Hilbert’s irreducibility theorem. In particular, we show that if f(X,T1,…,Ts) is an irreducible polynomial with integer coefficients, having Galois group G over the function field Q(T1,…,Ts), and K is any subgroup of G, then there are at most Of,ε(Hs−1+∣∣G/K∣∣−1+ε) specialisations t∈Zs with |t|≤H such that the resulting polynomial f(X) has Galois group K over the rationals.
Original languageEnglish
Pages (from-to)1-14
Number of pages14
JournalActa Arithmetica
Early online date9 Aug 2017
Publication statusE-pub ahead of print - 9 Aug 2017

Cite this