Probabilistic Galois Theory

Details Probabilistic Galois Theory Probabilistic Galois Theory

2011-11-11

arxiv.org/abs/1111.2853v1

Mathematics

Number Theory

10 pages

Scientific paper

We show that there are at most $O_{n,\epsilon}(H^{n-2+\sqrt{2}+\epsilon})$
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 $O_{n}(H^{n-1/2}\log H)$.

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