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arXiv · 1010.5341

On the distribution of Galois groups

Rainer Dietmann
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Abstract

Let $G$ be a subgroup of the symmetric group $S_n$, and let $δ_G=|S_n/G|^{-1}$ where $|S_n/G|$ is the index of $G$ in $S_n$. Then there are at most $O_{n, ε}(H^{n-1+δ_G+ε})$ monic integer polynomials of degree $n$ having Galois group $G$ and height not exceeding $H$, so there are only `few' polynomials having `small' Galois group.

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Rainer Dietmann. 2010-10-26. On the distribution of Galois groups. https://doi.org/10.1112/s0025579311002105

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