اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدQuantitative 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 Hilberts Irreducibility Theorem for degree $n$ polynomials $f$ with $mathrm{Gal}(f) subseteq A_n$. 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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