Hilbert's irreducibility theorem and the larger sieve

By David Zywina. 2010

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We describe an explicit version of Hilbert's irreducibility theorem using a generalization of Gallagher's larger sieve. We give applications to the Galois theory of random polynomials, and to the images of the adelic representation associated to elliptic curves varying in rational families.

View Paper: https://www.semanticscholar.org/paper/cd50c2d3fb0ce0c6a66ee629419b69165b30d5bc