Geodesic
PROBABILISTIC GALOIS THEORY FOR QUARTIC POLYNOMIALS
Glasgow mathematical journal, Tome 48 (2006) no. 3, pp. 553-556

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DOI

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 $O(H^{7/2} \log H)$.
DOI : 10.1017/S0017089506003272
Mots-clés : 11C08, 11R16, 11R32 
DIETMANN, RAINER. PROBABILISTIC GALOIS THEORY FOR QUARTIC POLYNOMIALS. Glasgow mathematical journal, Tome 48 (2006) no. 3, pp. 553-556. doi: 10.1017/S0017089506003272
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     title = {PROBABILISTIC {GALOIS} {THEORY} {FOR} {QUARTIC} {POLYNOMIALS}},
     journal = {Glasgow mathematical journal},
     pages = {553--556},
     year = {2006},
     volume = {48},
     number = {3},
     doi = {10.1017/S0017089506003272},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089506003272/}
}
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