On Hilbert's irreducibility theorem. / Castillo, Abel; Dietmann, Rainer.

In: Acta Arithmetica, Vol. 180, 09.08.2017, p. 1-14.

Research output: Contribution to journalArticlepeer-review

E-pub ahead of print

Abstract

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
Volume180
Early online date9 Aug 2017
DOIs
Publication statusE-pub ahead of print - 9 Aug 2017
This open access research output is licenced under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License.

ID: 27717497