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PROBABILISTIC GALOIS THEORY FOR QUARTIC POLYNOMIALS

Published online by Cambridge University Press:  06 December 2006

RAINER DIETMANN
RAINER DIETMANN
Affiliation:
Institut für Algebra und Zahlentheorie, Pfaffenwaldring 57, D-70550 Stuttgart, Germany e-mail: dietmarr@mathematik.uni-stuttgart.de
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Abstract

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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 $O(H^{7/2} \log H)$.

Keywords

11C0811R1611R32
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 48 , Issue 3 , September 2006 , pp. 553 - 556
Copyright
2006 Glasgow Mathematical Journal Trust