On the number of polynomials with small discriminants in the Euclidean and \(p\)-adic metrics

DOI10.1007/s10114-011-0518-5zbMath1275.11109OpenAlexW2044996376MaRDI QIDQ1758002

Natalia Budarina, Detta Dickinson, Jin Yuan

Publication date: 7 November 2012

Published in: Acta Mathematica Sinica. English Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10114-011-0518-5

zbMATH Keywords

Diophantine approximationdiscriminantpolynomial roots separation

Mathematics Subject Classification ID

Metric theory (11J83) Small fractional parts of polynomials and generalizations (11J54) Approximation in non-Archimedean valuations (11J61)

Related Items (4)

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 ⋮ New estimates for the number of integer polynomials with given discriminants

Cites Work

• Unnamed Item
• On the divisibility of the discriminant of an integral polynomial by prime powers
• Polynomial root separation examples
• An inequality for the discriminant of a polynomial
• \(S\)-arithmetic Khintchine-type theorem
• Root separation for irreducible integer polynomials
• Lower bounds for the number of integral polynomials with given order of discriminants
• POLYNOMIAL ROOT SEPARATION
• Simultaneous Diophantine approximation in the real, complex and p–adic fields.
• The distribution of close conjugate algebraic numbers

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