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ON THE DISTRIBUTION OF GALOIS GROUPS

Part of: Algebraic number theory: global fields Arithmetic algebraic geometry Polynomials and matrices

Published online by Cambridge University Press:  21 October 2011

Rainer Dietmann
Rainer Dietmann*
Affiliation:
Department of Mathematics, Royal Holloway, University of London, Egham, TW20 0EX, U.K. (email: Rainer.Dietmann@rhul.ac.uk)
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Abstract

Let G be a subgroup of the symmetric group Sn, and let δG=∣Sn/G∣−1 where ∣Sn/G∣ is the index of G in Sn. Then there are at most On,ϵ(Hn−1+δG+ϵ) monic integer polynomials of degree n that have Galois group G and height not exceeding H, so there are only a “few” polynomials having a “small” Galois group.

MSC classification

Secondary: 11C08: Polynomials 11R32: Galois theory 11G35: Varieties over global fields 11R45: Density theorems
Type
Research Article
Information
Mathematika , Volume 58 , Issue 1 , January 2012 , pp. 35 - 44
Copyright
Copyright © University College London 2012

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