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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1983 Springer Science+Business Media New York
About this chapter
Cite this chapter
Lang, S. (1983). Hilbert’s Irreducibility Theorem. In: Fundamentals of Diophantine Geometry. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-1810-2_9
Download citation
DOI: https://doi.org/10.1007/978-1-4757-1810-2_9
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4419-2818-4
Online ISBN: 978-1-4757-1810-2
eBook Packages: Springer Book Archive