On the divisibility of the discriminant of an integral polynomial by prime powers

DOI10.1007/S10986-008-9025-5zbMath1228.11111OpenAlexW1976074726MaRDI QIDQ736128

Friedrich Götze, Vasilii Bernik, Olga Kukso

Publication date: 27 October 2009

Published in: Lithuanian Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10986-008-9025-5

zbMATH Keywords

Diophantine approximationdiscriminantHaar measure\(p\)-adic valuation

Mathematics Subject Classification ID

Metric theory (11J83) Diophantine approximation in probabilistic number theory (11K60)

Related Items (7)

Integral polynomials with small discriminants and resultants ⋮ Simultaneous Diophantine approximation in two metrics and the distance between conjugate algebraic numbers in \(\mathbb C\times\mathbb Q_p\) ⋮ Discriminants of polynomials in the Archimedean and non-Archimedean metrics ⋮ On the number of polynomials with small discriminants in the Euclidean and \(p\)-adic metrics ⋮ The asymptotic number of integral cubic polynomials with bounded heights and discriminants ⋮ On the distribution of polynomial discriminants: totally real case ⋮ New estimates for the number of integer polynomials with given discriminants

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• Inhomogeneous diophantine approximation on polynomials in $ℚ_p$
• On approximation of real numbers by real algebraic numbers

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