On the distribution of Galois groups

Abstract

Let $G$ be a subgroup of the symmetric group $S_n$, and let ${\delta }_G=|S_n/G{|}^{-1}$ where $|S_n/G|$ is the index of $G$ in $S_n$. Then there are at most $O_{n,\epsilon }(H^{n-1+{\delta }_G+\epsilon })$ 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.

6 pages

References in corpus (2)

• Very simple 2-adic representations and hyperelliptic jacobians
• Hilbert's irreducibility theorem and the larger sieve

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