# 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} }

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

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Quantitative Hilbert irreducibility and almost prime values of polynomial discriminants

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We study two polynomial counting questions in arithmetic statistics via a combination of Fourier analytic and arithmetic methods. First, we obtain new quantitative forms of Hilbert’s Irreducibility… Expand

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