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On The Natural Density of Monic Integer Polynomials With Roots in A Fixed Number Field by xh0eql5vedyvwbncgxc is a document available to read on EtoBox.
This article explores the natural density and asymptotic behavior of monic integer polynomials of degree n with roots in a fixed number field K. It establishes that while the density of such polynomials is zero, the rate at which this density approaches zero varies with the degree, specifically showing a phase transition at degree n = 2. The study employs a combination of analytic and combinatorial methods to derive explicit bounds and asymptotic estimates for both reducible and irreducible polynomials, pro
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