Hilbert's irreducibility theorem and the larger sieve

Details Hilbert's irreducibility theorem and the larger sieve Hilbert's irreducibility theorem and the larger sieve

2010-11-30

arxiv.org/abs/1011.6465v1

Mathematics

Number Theory

Scientific paper

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.

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