Corpus ID: 235658465

# Towards van der Waerden's conjecture

@article{Chow2021TowardsVD,
title={Towards van der Waerden's conjecture},
author={Sam Chow and Rainer Dietmann},
journal={arXiv: Number Theory},
year={2021}
}
• Published 2021
• Mathematics
• arXiv: Number Theory
How often is a quintic polynomial solvable by radicals? We establish that the number of such polynomials, monic and irreducible with integer coefficients in $[-H,H]$, is $O(H^{3.91})$. More generally, we show that if $n \ge 3$ and $n \notin \{ 7, 8, 10 \}$ then there are $O(H^{n-1.017})$ monic, irreducible polynomials of degree $n$ with integer coefficients in $[-H,H]$ and Galois group not containing $A_n$. Save for the alternating group and degrees $7,8,10$, this establishes a 1936 conjecture… Expand
1 Citations
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