Hilbert’s Irreducibility Theorem
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In its simplest form, Hilbert’s theorem asserts : let f(t, X) be a polynomial in Q[f, X] (so in two variables), and assume that f(t, X) is irreducible. Then there exist infinitely many rational numbers t 0 such that f(t 0, X) is irreducible over Q.
KeywordsAbelian Variety Number Field Finite Type Finite Extension Quotient Field
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