On Hilbert’s Irreducibility Theorem
نویسندگان
چکیده
In this paper 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(H s−1+|G/K|+ε) specialisations t ∈ Zs with |t| ≤ H such that the resulting polynomial f(X) has Galois group K over the rationals.
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