Hilbert’s Irreducibility Theorem

Serge Lang
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Serge Lang: Yale University, Department of Mathematics

Chapter Chapter 9 in Fundamentals of Diophantine Geometry, 1983, pp 225-246 from Springer

Abstract: Abstract 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.

Keywords: Abelian Variety; Number Field; Finite Type; Finite Extension; Quotient Field (search for similar items in EconPapers)
Date: 1983
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DOI: 10.1007/978-1-4757-1810-2_9

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