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Creators/Authors contains: "Lemke Oliver, Robert J"

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  1. ; ; ; ; ; (, International Mathematics Research Notices)
    Abstract 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 Theorem for degree $$n$$ polynomials $$f$$ with $$\textrm {Gal}(f) \subseteq A_n$$. We study this both for monic polynomials and non-monic polynomials. Second, we study lower bounds on the number of degree $$n$$ monic polynomials with almost prime discriminants, as well as the closely related problem of lower bounds on the number of degree $$n$$ number fields with almost prime discriminants. 
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