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PROBABILISTIC GALOIS THEORY FOR QUARTIC POLYNOMIALS
Published online by Cambridge University Press: 06 December 2006
Abstract
We prove that there are only $O(H^{3+\epsilon})$ quartic integer polynomials with height at most $H$ and a Galois group which is a proper subgroup of $S_4$. This improves in the special case of degree four a bound by Gallagher that yielded $O(H^{7/2} \log H)$.
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- Research Article
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- 2006 Glasgow Mathematical Journal Trust
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