Name: Probabilistic Galois theory
Creator: Dietmann, Rainer
Keywords: Mathematics - Number Theory, FOS: Mathematics, Number Theory (math.NT), 0101 mathematics, 11C08, 11G35, 11R32, 11R45, 01 natural sciences

descriptionPublicationkeyboard_double_arrow_right Article , Preprint , Other literature type 20 Dec 2012Embargo end date: 01 Jan 2011 English Publisher:WileyJournal:Bulletin of the London Mathematical Society, volume 45, pages 453-462 (issn: 0024-6093,

Authors: Dietmann, Rainer;

doi: 10.1112/blms/bds113 , 10.48550/arxiv.1111.2853

arXiv: 1111.2853

Probabilistic Galois theory

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Abstract

We show that there are at most $O_{n,��}(H^{n-2+\sqrt{2}+��})$ monic integer polynomials of degree $n$ having height at most $H$ and Galois group different from the full symmetric group $S_n$, improving on the previous 1973 world record $O_{n}(H^{n-1/2}\log H)$.

10 pages

Related Organizations

Royal Holloway University of London
United Kingdom

Keywords

Mathematics - Number Theory, FOS: Mathematics, Number Theory (math.NT), 11C08, 11G35, 11R32, 11R45

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